Q. 4.25

Question

The two most commonly used scales for measuring temperature are the Fahrenheit and Celsius scales. If you let $y$ denote Fahrenheit temperature and $x$ denote Celsius temperature, you can express the relationship between those two scales with the linear equation $y = 32 + 1.8 x$
a. Determine $b_{0}$ and $b_{1}$
b. Find the Fahrenheit temperatures corresponding to the Celsius temperatures $- 40 °$ , $0 °$ , $20 °$ , and $100 °$ .
c. Graph the linear equation $y = 32 + 1.8 x$ , using the four points found in part (b).
d. Apply the graph obtained in part (c) to estimate visually the Fahrenheit temperature corresponding to a Celsius temperature of $28$ . Then calculate that temperature exactly by using the linear equation $y = 32 + 1.8 x$

Step-by-Step Solution

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Answer

Part(a)The value of $b_{0} = 32, b_{1} = 1.8$

Part(b) The Fahrenheit temperature for corresponding Celsius temperature $- 40 °, 0 °, 20 °, 100 °$ are $- 40 ° F, 32 ° F, 68 ° F, 212 ° F$ respectively.

Part(c) Required figure is given below.

Part(d) Required figure is given below . and $28 ° C$ is $82.4 ° F$

1Part(a) Step 1: Given information

We are given an equation that can express the relationship between two scales Fahrenheit and Celsius scale. We have to determine $b_{0}$ and $b_{1}$

2Part(a) Step 2: Simplify

Given equation is $y = 32 + 1.8 x$

Where,

$y =$ Fahrenheit scale

$x =$ Celsius scale

$b_{0} =$ Intercept

$b_{1} =$ Slope

According to equation

$b_{0} = 32 b_{1} = 1.8$

3Part(b) Step 1: Given information

We are given an equation that can express the relationship between two scales Fahrenheit and Celsius scale .

4Part(b) Step 2: Simplify

Equation is $y = 32 + 1.8 x$

Where,

$y =$ Fahrenheit scale

$x =$ Celsius scale

Now,

$x = - 40 ° y = 32 + 1.8 (- 40) = - 40 ° F x = 0 ° y = 32 + 1.8 (0) = 32 ° F x = 20 ° y = 32 + 1.8 (20) = 68 ° F x = 100 ° y = 32 + 1.8 (100) = 212 ° F$