Find the linear equation that models the price-sales relationship for this Frisbee.

Question

The Whammo Company has learned that by pricing a newly Frisbee at $6, sales will reach 2000 per day. Raising the price to $8 will cause the sales to fall to 1500 per day. Assume that the ratio of change in price to change in daily sales is constant and let x be the price of the Frisbee and y be number of sales.

Answer 1

Given two points

($6, 2000 sales/day)

($8,1500 sales/day)

 

The slope is change in y over change in x 

 

m=(2000-1500)/(6-8)=-250

 

equation of a line with slope m is:

 

y=-250x+ b

 

Use one of the points to solve for b (y intercept)

 

2000=-250(6)+b

3500=b

 

Note the other point will yield the same b. You only need one point (either point) to solve for b. 

 

The linear relationship is:

 

y=-250x+3500

 

Check your work by making sure the original points when plugged into this line equation yield truth.