Question

The equation y = 50 + 40x models the charge for his services y for any number of hours x. a.Graph the equation b. What is the slope of the line? What does the slope represent? c. What is the y-intercept of the line? What does the y-intercept represent?

David does landscaping for private homes. He charges $50 to travel to the site and then $40 per hour for his services. The equation y = 50 + 40x models the charge for his services y for any number of hours x.

Answer 1

Please see below.

Explanation:

.

`color(red)(a))`

`y=50+40x`

The graph is shown below:

As you can see the line is very steep and hard to distinguish from the `y`-axis. Let's look at the graph where I have given the `x`-axis larger scale than the `y`-axis to make the graph more visible.

`color(red)(b))`

Let's write the equation in the slope-intercept form which is:

`y=mx+b` where `m` is the slope and `b` is the `y`-intercept.

`y=40x+50`

The slope of the line is `m=40`. The slope represents the rate at which the cost of service increases with the increase in time (hours).

`color(red)(c))`

The `y`-intercept of the line is `b=50`. It represents the initial charge at the time the service work starts.