Question

18. Recall that 0°C = 32°F and 100°C = 212°F.

a. Using x for degrees Celsius and y for degrees Fahrenheit, find
an equation of the line passing through (0, 32) and (100, 212).
b. What is the slope of the line? Explain what the slope means in
terms of degrees Celsius and degrees Fahrenheit.
c. What is the y-intercept of the line? Explain what the y-intercept
means in terms of degrees Celsius and degrees Fahrenheit.​

Answer 1

Part a) The equation of the line is

`y-32=1.8(x-0)` or
`y=1.8x+32`

Part b) The slope of the line is
`m=1.8(\°F)/(\°C)`

Part c) The y-intercept is 32 (For a degrees Celsius equal to zero, the degrees Fahrenheit is equal to 32)

Explanation:

Let

x ----> degrees Celsius

y ----> degrees Fahrenheit

we have the points

`(0,32),(100,212)`

Part a) Find the equation of the line

Find the slope m

`m=(212-32)/(100-0)`

`m=180/100`

`m=1.8(\°F)/(\°C)`

The equation of the line into slope point form is equal to

`y-y1=m(x-x1)`

we have

`m=1.8(\°F)/(\°C)`

Point
`(0,32)`

substitute

`y-32=1.8(x-0)` ----> equation of the line into slope point form

`y=1.8x+32` ---> equation of the line into slope intercept form

Part b) What is the slope of the line?

The slope of the line is
`m=1.8(\°F)/(\°C)`

That means

The rate of change of the temperature is 1.8 degrees Fahrenheit by each degree Celsius

Part c) What is the y-intercept of the line?

we have

`y=1.8x+32` ---> equation of the line into slope intercept form

The y-intercept is 32

The y-intercept is the value of y when the value of x is equal to zero

That means

For a degrees Celsius equal to zero, the degrees Fahrenheit is equal to 32