Question

Solve.

A vendor has learned that, by pricing pretzels at $1.00, sales will reach 92 pretzels per day. Raising the price to $1.50 will cause the sales to fall to 72 pretzels per day. Let y be the number of pretzels the vendor sells at x dollars each. Write a linear equation that models the number of pretzels sold per day when the price is x dollars each.
A) y = 40x + 52
B) y = -40x + 132
C) y = - 1/40x + 3679/40
D) y = -40x - 132

Answer 1

If you can filter through all the words, you might notice that they are giving you two ordered pairs for (x,y) = (price, # of pretzels sold)

The first sentence gives you ($1, 92 pretzels) or (1,92)

The next sentence gives you (1.50, 72)

Think back when you wrote equations of lines using two points... you need to find a slope and the y intercept. You can find slope by comparing the change in pretzels sold divided by the change in price.

Answer 2

so y1-y2/x1-x2

Answer 3

ok so i got -40x now what

Answer 4

98-72/1-1.50

Answer 5

you can then write a point-slope equation as a way of getting to the slope-intercept form that the answers are shown in.

Point slope form of a line is y - y1 = m(x - x1) where (x1, y1) is one of your points, and you already know m.

Then simplify it down to get it like y = mx + b

Answer 6

ok

Answer 7

so y-92=-40(x-1)

Answer 8

b) y=-40x+132

Answer 9

looks good :) Quick double check... put in your two points and see if they both work.

Answer 10

y = -40($1) + 132 = 92 pretzels (WORKS)
y = -40(1.50) + 132 = 72 pretzels (WORKS)

Answer 11

nice work :)

Answer 12

thankyou

Answer 13

you are welcome, glad to help :)