Question

A vendor has learned that, by pricing caramel apples at $1.25, sales will reach 111 caramel apples per day. Raising the price to $2.00 will cause the sales to fall to 81 caramel apples per day. Let y be the number of caramel apples the vendor sells at x dollars each. The linear equation y = -40x + 161 models the number of caramel apples sold per day when the price is x dollars each. Interpret the slope.

Answer 1

Solution:

Slope = y2 - y1 / x2 -x1

slope = 81 - 111 / $2.00 - $1.25

slope = -30/$0.75

So every $0.75 increase causes a decrease of 30 sales.

So the rise over run or slope of the line is -30/0.75 = -40/1

Start forming the equation:

y = mx + b

y = -40x + b

Substitute one of the points to find the y-intercept:

81 = -40(2) + b

Isolate for the y-intercept:

b = 161

So,

y = -40x + 161