{"id":2139,"date":"2026-05-25T14:04:35","date_gmt":"2026-05-25T08:34:35","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=2139"},"modified":"2026-05-25T14:04:39","modified_gmt":"2026-05-25T08:34:39","slug":"ncert-class-9-maths-exercise-2-5-solutions-linear-relationships","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-9-maths-exercise-2-5-solutions-linear-relationships\/","title":{"rendered":"NCERT Class 9 Maths Exercise 2.5 Solutions \u2013 Linear Relationships"},"content":{"rendered":"<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2139?print=pdf\" class=\"pdfprnt-button pdfprnt-button-pdf\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/pdf.png\" alt=\"image_pdf\" title=\"Download PDF\" \/><span class=\"pdfprnt-button-title pdfprnt-button-pdf-title\">Save as PDF<\/span><\/a><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2139?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\" \/><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\"><\/span><\/div>\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Short Intro<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Exercise 2.5 introduces the concept of <strong>linear relationships<\/strong> between two variables using equations of the form <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>a<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y = ax + b<\/annotation><\/semantics><\/math>. These questions help students understand how real-life situations like internet bills, gym charges, and temperature conversion can be represented mathematically.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Quick Information Box<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Topic<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Chapter<\/td><td>Introduction to Linear Polynomials<\/td><\/tr><tr><td>Exercise<\/td><td>Exercise 2.5<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Class<\/td><td>Grade 9<\/td><\/tr><tr><td>Main Concepts<\/td><td>Linear Relationships<\/td><\/tr><tr><td>Difficulty Level<\/td><td>Moderate<\/td><\/tr><tr><td>Useful For<\/td><td>School Exams &amp; Olympiad Preparation<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Concepts Used (Topics Covered)<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Linear Relationships<\/li>\n\n\n\n<li>Linear Equations<\/li>\n\n\n\n<li>Slope and Intercept<\/li>\n\n\n\n<li>Variable Relationships<\/li>\n\n\n\n<li>Equation Formation<\/li>\n\n\n\n<li>Algebraic Substitution<\/li>\n\n\n\n<li>Real-life Mathematical Modelling<\/li>\n\n\n\n<li>Temperature Conversion<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Important Formulas<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">General Linear Equation<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>a<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y=ax+b<\/annotation><\/semantics><\/math>y=ax+b<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"325\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-29-1024x325.png\" alt=\"image\" class=\"wp-image-2140\" title=\"NCERT Class 9 Maths Exercise 2.5 Solutions \u2013 Linear Relationships\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-29-1024x325.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-29-300x95.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-29-768x243.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-29.png 1167w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">a<\/annotation><\/semantics><\/math>= slope\/rate of change<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">b<\/annotation><\/semantics><\/math> = fixed value or intercept<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Celsius\u2013Fahrenheit Relation<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><mi>a<\/mi><mi>F<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C=aF+b<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Solving Simultaneous Equations<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute one equation into another to find unknown values.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Questions &amp; Step-by-Step Solutions<\/h1>\n\n\n\n<h1 class=\"wp-block-heading\">Question 1<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">A learning platform charges a fixed monthly fee and an additional cost per digital learning module accessed. A student observes that when she accessed 10 modules, her bill was \u20b9400. When she accessed 14 modules, her bill was \u20b9500. If the monthly bill <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y<\/annotation><\/semantics><\/math>y depends on the number of modules accessed <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math>x, according to the relation <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>a<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y=ax+b<\/annotation><\/semantics><\/math>y=ax+b, find the values of <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">a<\/annotation><\/semantics><\/math>a and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">b<\/annotation><\/semantics><\/math>b.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>10<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x=10<\/annotation><\/semantics><\/math>, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mn>400<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y=400<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>400<\/mn><mo>=<\/mo><mn>10<\/mn><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">400 = 10a + b<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>14<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x=14<\/annotation><\/semantics><\/math>, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mn>500<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y=500<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>500<\/mn><mo>=<\/mo><mn>14<\/mn><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">500 = 14a + b<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Subtract equations:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>500<\/mn><mo>\u2212<\/mo><mn>400<\/mn><mo>=<\/mo><mn>14<\/mn><mi>a<\/mi><mo>\u2212<\/mo><mn>10<\/mn><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">500 &#8211; 400 = 14a &#8211; 10a<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>100<\/mn><mo>=<\/mo><mn>4<\/mn><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">100 = 4a<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mn>25<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a = 25<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute into first equation:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>400<\/mn><mo>=<\/mo><mn>10<\/mn><mo stretchy=\"false\">(<\/mo><mn>25<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">400 = 10(25) + b<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>400<\/mn><mo>=<\/mo><mn>250<\/mn><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">400 = 250 + b<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>b<\/mi><mo>=<\/mo><mn>150<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">b = 150<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Final Answer<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mn>25<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a = 25<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>b<\/mi><mo>=<\/mo><mn>150<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">b = 150<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Linear Relationship<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mn>25<\/mn><mi>x<\/mi><mo>+<\/mo><mn>150<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y = 25x + 150<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 2<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">A gym charges a fixed monthly fee and an additional cost per hour for using the badminton court. A student observed that when she used the badminton court for 10 hours, her bill was \u20b9800. When she used it for 15 hours, her bill was \u20b91100. If the monthly bill <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y<\/annotation><\/semantics><\/math>y depends on the hours of use <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math>x, according to the relation <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>a<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y=ax+b<\/annotation><\/semantics><\/math>y=ax+b, find the values of <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">a<\/annotation><\/semantics><\/math>a and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">b<\/annotation><\/semantics><\/math>b.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>10<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x=10<\/annotation><\/semantics><\/math>, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mn>800<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y=800<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>800<\/mn><mo>=<\/mo><mn>10<\/mn><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">800 = 10a + b<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>15<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x=15<\/annotation><\/semantics><\/math>, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mn>1100<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y=1100<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>1100<\/mn><mo>=<\/mo><mn>15<\/mn><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">1100 = 15a + b<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Subtract equations:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>300<\/mn><mo>=<\/mo><mn>5<\/mn><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">300 = 5a<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mn>60<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a = 60<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute into first equation:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>800<\/mn><mo>=<\/mo><mn>10<\/mn><mo stretchy=\"false\">(<\/mo><mn>60<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">800 = 10(60) + b<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>800<\/mn><mo>=<\/mo><mn>600<\/mn><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">800 = 600 + b<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>b<\/mi><mo>=<\/mo><mn>200<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">b = 200<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Final Answer<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mn>60<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a = 60<\/annotation><\/semantics><\/math>a=60<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>b<\/mi><mo>=<\/mo><mn>200<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">b = 200<\/annotation><\/semantics><\/math>b=200<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Linear Relationship<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mn>60<\/mn><mi>x<\/mi><mo>+<\/mo><mn>200<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y = 60x + 200<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 3<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Consider the relationship between temperature measured in degrees Celsius (\u00b0C) and degrees Fahrenheit (\u00b0F), which is given by:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u00b0<\/mi><mi>C<\/mi><mo>=<\/mo><mi>a<\/mi><mi mathvariant=\"normal\">\u00b0<\/mi><mi>F<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\u00b0C = a\u00b0F + b<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Find <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">a<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">b<\/annotation><\/semantics><\/math>, given that ice melts at <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>0<\/mn><mi mathvariant=\"normal\">\u00b0<\/mi><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">0\u00b0C<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>32<\/mn><mi mathvariant=\"normal\">\u00b0<\/mi><mi>F<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">32\u00b0F<\/annotation><\/semantics><\/math>, and water boils at <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>100<\/mn><mi mathvariant=\"normal\">\u00b0<\/mi><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">100\u00b0C<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>212<\/mn><mi mathvariant=\"normal\">\u00b0<\/mi><mi>F<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">212\u00b0F<\/annotation><\/semantics><\/math>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>F<\/mi><mo>=<\/mo><mn>32<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">F=32<\/annotation><\/semantics><\/math>, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">C=0<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>0<\/mn><mo>=<\/mo><mn>32<\/mn><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">0 = 32a + b<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>F<\/mi><mo>=<\/mo><mn>212<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">F=212<\/annotation><\/semantics><\/math>, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><mn>100<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">C=100<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>100<\/mn><mo>=<\/mo><mn>212<\/mn><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">100 = 212a + b<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Subtract equations:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>100<\/mn><mo>=<\/mo><mn>180<\/mn><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">100 = 180a<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mfrac><mn>100<\/mn><mn>180<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">a = \\frac{100}{180}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mfrac><mn>5<\/mn><mn>9<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">a = \\frac{5}{9}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute into first equation:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>0<\/mn><mo>=<\/mo><mn>32<\/mn><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>5<\/mn><mn>9<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">0 = 32\\left(\\frac{5}{9}\\right) + b<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>b<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>160<\/mn><mn>9<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">b = -\\frac{160}{9}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Final Answer<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mfrac><mn>5<\/mn><mn>9<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">a = \\frac{5}{9}<\/annotation><\/semantics><\/math>\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>b<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mfrac><mn>160<\/mn><mn>9<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">b = -\\frac{160}{9}<\/annotation><\/semantics><\/math>\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Linear Relationship<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><mfrac><mn>5<\/mn><mn>9<\/mn><\/mfrac><mo stretchy=\"false\">(<\/mo><mi>F<\/mi><mo>\u2212<\/mo><mn>32<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">C=\\frac{5}{9}(F-32)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\u274c Forgetting to substitute values correctly<br>\u274c Sign errors while subtracting equations<br>\u274c Confusing fixed charge with variable charge<br>\u274c Incorrect fraction simplification<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Exam Tips<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\u2714 Write equations clearly before solving<br>\u2714 Use elimination or substitution method carefully<br>\u2714 Verify answers by substituting values back<br>\u2714 Remember slope represents rate of change<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Practice MCQs<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">1. Which equation represents a linear relationship?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y=x^2+1<\/annotation><\/semantics><\/math><br>B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y=3x+2<\/annotation><\/semantics><\/math><br>C) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><msup><mn>2<\/mn><mi>x<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">y=2^x<\/annotation><\/semantics><\/math><br>D) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><msup><mi>x<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">y=x^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y=3x+2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">2. In <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>a<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y=ax+b<\/annotation><\/semantics><\/math>, what does <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">a<\/annotation><\/semantics><\/math> represent?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) Constant term<br>B) Slope<br>C) Variable<br>D) Intercept<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 B) Slope<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">3. In <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>a<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y=ax+b<\/annotation><\/semantics><\/math>, what does <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">b<\/annotation><\/semantics><\/math> represent?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) Slope<br>B) Variable<br>C) y-intercept<br>D) Equation degree<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 C) y-intercept<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">4. Which relation converts Fahrenheit to Celsius?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><mi>F<\/mi><mo>+<\/mo><mn>32<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">C=F+32<\/annotation><\/semantics><\/math><br>B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><mfrac><mn>5<\/mn><mn>9<\/mn><\/mfrac><mo stretchy=\"false\">(<\/mo><mi>F<\/mi><mo>\u2212<\/mo><mn>32<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">C=\\frac{5}{9}(F-32)<\/annotation><\/semantics><\/math><br>C) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><mn>2<\/mn><mi>F<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C=2F<\/annotation><\/semantics><\/math><br>D) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><mi>F<\/mi><mo>\u2212<\/mo><mn>100<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">C=F-100<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 B) <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><mfrac><mn>5<\/mn><mn>9<\/mn><\/mfrac><mo stretchy=\"false\">(<\/mo><mi>F<\/mi><mo>\u2212<\/mo><mn>32<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">C=\\frac{5}{9}(F-32)<\/annotation><\/semantics><\/math> <\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">FAQ Section<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Q1. What is a linear relationship?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A linear relationship is a relationship between two variables represented by a straight-line equation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. What is the standard form of a linear equation?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The standard form is:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>a<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y=ax+b<\/annotation><\/semantics><\/math> <\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. What does slope mean?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Slope represents the rate at which one quantity changes compared to another.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q4. What is y-intercept?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">It is the point where the graph cuts the y-axis.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q5. Why are linear equations important?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">They help represent real-life situations mathematically.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">Practice more chapter-wise Maths solutions, MCQs, mock tests, and exam-oriented study material on <strong><a target=\"_blank\" rel=\"noreferrer noopener\">MyMockMate<\/a><\/strong> and strengthen your Class 9 Mathematics concepts with smart learning tools!<audio autoplay=\"\"><\/audio><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2139?print=pdf\" class=\"pdfprnt-button pdfprnt-button-pdf\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/pdf.png\" alt=\"image_pdf\" title=\"Download PDF\" \/><span class=\"pdfprnt-button-title pdfprnt-button-pdf-title\">Save as PDF<\/span><\/a><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2139?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\" ><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\" \/><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\"><\/span><\/div>\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n","protected":false},"excerpt":{"rendered":"<p> Short Intro Exercise 2.5 introduces the concept of linear relationships between two variables using equations<\/p>\n","protected":false},"author":1,"featured_media":2141,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_surecart_dashboard_logo_width":"180px","_surecart_dashboard_show_logo":true,"_surecart_dashboard_navigation_orders":true,"_surecart_dashboard_navigation_invoices":true,"_surecart_dashboard_navigation_subscriptions":true,"_surecart_dashboard_navigation_downloads":true,"_surecart_dashboard_navigation_billing":true,"_surecart_dashboard_navigation_account":true,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[22,4,11],"tags":[718,719,136,714,685,720,679,723,669,715,91,674,721,722,673,717,716],"class_list":["post-2139","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse","category-class-9","category-maths-class-9","tag-algebraic-relationships","tag-class-9-algebra-solutions","tag-class-9-maths","tag-exercise-2-5-solutions","tag-grade-9-mathematics","tag-graph-equations-maths","tag-linear-equations","tag-linear-function-problems","tag-linear-polynomial-chapter","tag-linear-relationships","tag-maths-chapter-2-solutions","tag-mymockmate-maths-solutions","tag-relationship-between-variables","tag-slope-and-intercept","tag-step-by-step-maths-solutions","tag-temperature-conversion-maths","tag-yaxb-questions"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2139","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/comments?post=2139"}],"version-history":[{"count":1,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2139\/revisions"}],"predecessor-version":[{"id":2142,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/2139\/revisions\/2142"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/2141"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=2139"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=2139"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=2139"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}