Another math question that I don't get

The Whammo company has learned that by pricing a newly released Frisbee at $6, the sales will reach 2000 per day. Raising the price to $8 will cause the sales to fall to 1500 per day. Assume that the cost and sales are linearly related and let "x" be the price of the Frisbee and "y" be the number of sales.

a. Find a linear equation that models this price-sales relationship.

b. Use the equation to price the daily sales of Frisbees if the price is set at $7.50.

Can you show work, too?

If it is linear, then the equation is y = mx+b.

You have 2 points along the line, x is price, y is sales, so you have (6,2000) and (8,1500) so:

2000 = 6m+b and 1500 = 8m+b
b = 2000 - 6m, put that in the 2nd equation:

1500 = 8m + 2000 - 6m
-500 = 2m
-250 =m

put that into either equation:
2000 = 6(-250) +b
2000 = -1500 +b
3500 = b, so:

y = -250x + 3500
if the price is 7.50:
y = -250 (7.5) + 3500
y = 1625

So we know that the linear equation should pass through the points ($6, 2000 frisbees) and ($8, 1500 frisbees). We can define a line using those two points.

First, we need a slope: That will represent how fast the sales change as price changes. We find it to be
slope = change in sales/ change in price = (2000 - 1500 ) / (6-8) = 500/-2 = -250 frisbees/dollar

So the line will be Sales = -250(price) + b, where b represents how many would be sold if the frisbees were free. To find b, we need to plug in a point we know. Let's use (6, 2000). According to our model,

2000 frisbees = -250(6) frisbees + b
2000 = -1500 + b
3500 = b

So our final model: y=-250x + 3500

b) Now to find the daily sales of frisbees if the price is 7.50, we just need to plug 7.50 in for x:

y = -250(7.50) + 3500 = -1875 + 3500 = 1625 frisbees.