Question

The table shows the relationship between the cost of renting a car from the Wrecko Car Rental Company and the number of days for the rental. Draw a scatter plot and find an equation for the line of best fit. Use the equation to determine the cost of renting a car for 20 days. Days Cost 1 $44 2 $67 3 $90 4 $113 7 $182 10 $251

Answer 1

The cost of renting the car for 20 days is $481

Explanation:

The table of values can be formed as follows;

Day, Cost

1, $44

2, $67

3, $90

4, $113

7, $182

10, $251

From the given values and the scatter plot, there is a straight line relationship between the cost and the number of days of rental of a car.

The line of best fit is therefore a straight line and from the constant increase in cost ($23) for each extra day of rental, it is possible to find the slope, m, of the data as follows;

`Slope, \, m =(y_(2)-y_(1))/(x_(2)-x_(1))`

(x₁, y,) and (x₂, y₂) can be taken as (1, $44) and (3, $90) respectively to give;

`Slope, \, m =(90-44)/(3-1) = (46)/(2) = 23 \ as \ stated \ above`

The equation in slope and intercept form is therefore, y - 44 = 23×(x - 1), which gives;

y - 44 = 23·x - 23

y = 23·x - 23 + 44 = 23·x + 21

The cost of renting the car for 20 days is then;

10×23 + 21 = $481

The cost of renting the car for 20 days = $481.