Question

The table shows how much an air-conditioning repair company charges for different numbers of hours of work. Graph the the data, and find the slope and y-intercept from the graph. Then write the equation for the graph in slope-intercept form.

Answer 1

Slope=$50 per hour of air-conditioning repair.

y-intercept= 50.

Equation for the graph in slope-intercept form=
`y=50x+50`

Step-by-step explanation:

We have been given a table that shows how much an air-conditioning repair company charges for different numbers of hours of work. We are asked to graph the data.

A. First of all we will plot the points on our graph. After plotting points we will join all the points to form a line.

Please find the attachment for the graph of our given data.

B. Let us find slope of our given data using slope formula.

`m=(y_2-y_1)/(x_2-x_1)`

m= Slope.

`y_2-y_1`= Difference between two y-coordinates or vertical change.

`x_2-x_1`= Difference between corresponding x-coordinates or horizontal change.

Upon substituting two y-coordinates and their corresponding x-coordinates in slope formula, we will get,

`m=(300-50)/(5-0)`

`m=(250)/(5)`

`m=50`

Therefore, slope of the our given function is $50 per hour of air-conditioning repair.

C. Since the y-intercept is initial value of function. At y-intercept x equals zero.

We can see from our graph that at y equals 50, x equals zero, therefore, y-intercept is 50.

Since the equation for a line in slope-intercept form is:
`y=mx+b`, where,

m=Slope of the line.

b= y-intercept.

Upon substituting m=50 and b=50 in slope-intercept form of equation we will get,

`y=50x+50`

Therefore, the equation of our given graph in slope-intercept form will be
`y=50x+50`.