Using the relation C = aF + b, substitute the given conditions. From the melting point, 0 = 32a + b. From the boiling point, 100 = 212a + b. Solving this gives a = 5/9 and b = -160/9.
Consider the relationship between temperature measured in degrees Celsius (°C) and degrees Fahrenheit (°F), which is given by °C = a °F + b. Find a and b, given that ice melts at 0 degrees Celsius and 32 degrees Fahrenheit and water boils at 100 degrees Celsius and 212 degrees Fahrenheit. (Hint: When °C = 0, °F = 32 and when °C = 100, °F = 212. Use this information to find a and b and thus, the linear relationship between °C and °F.)
Share
Substitute the temperature coordinates into the linear relationship C = aF + b. For the melting point, 0 = 32a + b, which means b = -32a. For the boiling point, 100 = 212a + b. Substituting b into the second equation yields 100 = 212a – 32a, which simplifies to 100 = 180a. This gives a = 100/180 = 5/9. Using a to find b gives b = -160/9. The values are a = 5/9 and b = -160/9.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 2 Introduction to Linear Polynomials (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-2/