Question

Car Sales A manufacturer of economy cars has determined that 50,000 cars per month can be sold at a price of $18,000 per car. At a price of $17,500, the number of cars sold per month would increase to 55,000. Determine a linear function that predicts the number of cars that will be sold at a price of x dollars. Use this model to predict the number of cars that will be sold at a price of $17,000.

Answer 1

Answer: 60,000 cars would be sold at $17000.

Explanation:

• first we find the slope of the function between two points

(50,000, 18000) and ( 55,000, 17500)

• Let the number of cars sold be the x axis coordinate.

and the price is the y axis coordinate.

• next we plot this points.

m= Change in y / Change in x = rise / run

The slope m = (18000 - 17500/ 50,000 - 55,000)

= -0.1

• The equation of the line in point slope form is m(x-x1)=(y-y1)

• substituting for the first point

-0.1 (X-50,000) = y-18000

-0.1x - 5000 = y - 18000

-0.1x = 18000 + 5000

y = -0.1x + 23000

our slope -0.1 is negative.

In order to find the number of cars to be sold at a price of $17000, substitute this value y in the equation such that:

17000 =-0.1x+23000

solve for x

-0.1x = 23000-17000

0.1x = 6000

divide both sides by 0.1

x = 60000

60,000 cars would be sold at $17,000