Question

Sam and Sully are electricians. The graph represents the amount in dollars that Sam charges in terms of the number of hours he works. The amount in dollars that Sully charges in terms of the number of hours he works is represented by the function y = 22x + 36. The initial amount Sam charges is BLANK the initial amount Sully charges. Sam’s hourly rate is BLANK Sully’s hourly rate.

Answer 1

Answer:

The initial amount Sam charges is [$4 greater than] the initial amount Sully charges. Sam’s hourly rate is [$2 less than] Sully’s hourly rate.

A graph is attached for reference.

Step-by-step explanation:

Given is the graph that represents the amount in dollars that Sam charges in terms of the number of hours he works.

Where two points are (0,40) and (1,60).

Finding the slope,

$m=\frac{(y2-y1)}{(x2-x1)} \\m=\frac{(60-40)}{(1-0)} \\m=\frac{20}{1} \\m=20$

Let us find the equation now,

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

Substituting (0,40) as (x1,y1) and slope m = 20

$y-40=20(x-0)\\y-40 = 20x\\y= 20x+40$

Here the 'y' intercept $40$ represents the initial charge of Sam.

On comparing the equations of Sam and Sully we observe that Sam initial charge is $40$  dollars.

And Sully's initial charge is $36$  dollars.

Thus Sam's initial charge is $4 greater than Sully's.

Similarly,

Slope represents their per hour charge.

The coefficient of 'x' represents their slope,

Slope in case of Sam,

$y=20x+40$ is $'20'$

And

Slope in case of Sully,

$y=22x+36$ is $'22'$

Thus on observing the slope 20 and 22, we say that the per hour charge of Sam is $2 less than that of Sully's.