Question

The cost of driving a rental car depends on the number of miles driven. Marc rented a car and drove it 250 miles in one week. This cost him $130. The next week, he rented the same car and drove it 700 miles. This cost him $220. Assume that there is a linear relationship between the cost C of a rental car and the miles driven d.

Find a linear equation that relates C and d

What does the y intercept of the graph represent?

Answer 1

Given : 250 miles cost $130 and 700 miles cost $220.

Variables d and C are taken for distance travelled in miles and cost of a rental car.

The coordinates of the given problem could be written in the form.

(distance, cost) = (d,c).

For the given statements, we can make two coordinates (250,130) and (700, 220)

In order to find the linear equation, we need to find the slope first.

We know formula for slope

$m=\frac{y_2-y_2}{x_2-x_1}$

For coordinates (250,130) and (700, 220), we have x1=250, y1 = 130, x2 = 700 and y2 = 220.

Plugging those values in slope formula, we get

$m=\frac{220-130}{700-250}=\frac{90}{450}=\frac{1}{5}$

So, the slope of the line m= 1/5.

Now appying point-slope form

y-y1= m(x-x1)

y-130=1/5(x-250).

y-130 = 1/5x - 50

Adding 130 on both sides, we get

y-130+130 = 1/5x - 50+130

y= 1/5x + 80.

If we compare y=1/5x +80 with slope-intercept form y=mx+b, we can see that b=80.

Therefore, y-intercept is 80.

In the given problem variables d and C are taken for x and y.

Replacing x and y by d and C, we get

C= 1/5d + 80.

As we got y-intercept 80. y-intercept represents fix cost of car rented and that is $80.