Question

How do i answer part b

Answer 1

Answer: The slope is the cost per hour (in this case $20 per hour).

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Further Explanation:

Recall that,

`\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}`

The rise tells us how much to go up or down, depending if the rise is positive or negative. The run tells us how much to go to the right. Always move to the right.

In this problem, the change in y is the change in price. The change in x is the change in hours. Dividing the two items gives cost per hour, aka unit cost.

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Example:

Let's pick two points from this line and use the slope formula. I'll pick (1,60) and (3,100) as they are the only two points with coordinate labels.

So,

`(x_1,y_1) = (1,60) \text{ and } (x_2,y_2) = (3,100)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_(2) - \text{y}_(1)}{\text{x}_(2) - \text{x}_(1)}\\\\m = (100 - 60)/(3 - 1)\\\\m = (40)/(2)\\\\m = 20\\\\`

The slope is 20, or 20/1

It says that each time the number of hours x goes up by 1, the cost variable y goes up by 20.

Put simply: The hourly fee is $20 per hour.

This matches what it says in the instructions when your teacher wrote "A roofer charges $60 for the first hour and $20 per hour for each additional hour".