Question 1176812: Solve.
A vendor has learned that, by pricing hot dogs at $1.00, sales will reach 119 hot dogs per day. Raising the price to $1.50 will cause the sales to fall to 95 hot dogs per day. Let y be the number of hot dogs the vendor sells at x dollars each. Write a linear equation that models the number of hot dogs sold per day when the price is x dollars each.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the straight line equation to use is y = mx + b.
y is the number of hotdogs sold.
x is the price of each hotdog.
m is the slope
b is the y-intercept
when x = 1, y = 119
when x = 1.5, y = 95
the slope is equal to (y2-y1) / (x2-x1), where (x2,y2) = (1,119) and (x1,y1) = 1.5,95)
the equation becomes y = (119-95)/(1-1.5) = -24/.5 = -48.
the equation becomes y = -48x + b
use any of the point pairs used to create the slope to replace x and y in the equation so you can solve for b.
i chose (1,119),
the equation becomes 119 = -48 * 1 + b
solve for b to get b = 119 + 48 = 167.
the equation becomes y = -48x + 167.
when x = 1, y = -48 * 1 + 167 = 119.
when x = 1.5, y = -48 * 1.5 + 167 = 95.
the equation is confirmed to be good.
your solution is that the equation to model the number of hotdogs sold each day when the price is x dollars each is y = -48x + 167.
on a graph, the equation looks like this.
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