Question

A vendor has learned that, by pricing ? his deep fried bananas on a stick at $1.50?, sales will reach 110? per day. Raising the price to $2.50? will cause the sales to fall to ?70? per day. Let y be the number of ? the vendor sells at x dollars each. Write a linear equation that models the number of ? sold per day when the price is x dollars each. The linear equation is y = .

Answer 1

y = -40*x + 170

Explanation:

Data

When price is $1.50 per banana, sales reach 110 per day

When price is $2.50 per banana, sales reach 70 per day

Calling y the number of deep fried bananas on a stick per day the vendor sells and x its price in dollars per banana; the above data can be expressed as points (x1, y1) and (x2, y2), i. e., (1.5, 110) and (2.5, 70). The question asks for a linear expression to represent given points. General linear formula is:

y = m*x + b

where m is the slope and b is the y-intercept.

Slope is computed as follows

m = (y2 -y1)/(x2 -x1) = (70 - 110)/(2.5 - 1.5) =-40

y-intercept is computed replacing general formula with a known point and the slope, as follows

y1 = m*x1 + b

110 = -40*1.5 + b

110 + 60 = b

170 = b

Therefore, the linear equation is: y = -40*x + 170