Question 1107488: As a salesperson at Roaring Waves Beach Supplies, Carissa receives a monthly based pay plus commission on all that she sells. If she sells $500 worth of merchandise in one month, she is paid $390. If she sells $1,000 worth of merchandise in one month, she gets paid $480. Find Carissa's salary when she sells $2,400 worth of merchandise?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let y equal the revenue.
let x equal the dollar amount of merchandise she sells in a month.
slope intercept form of a straight line equation is y = mx + b.
m is the slope which is the change in y divided by the change in x.
b is the y-intercept which is the value of y when the value of x is 0.
if she sells 500 in one month, she makes 390.
if she sells 1000 in one month, she makes 480.
when she sells 500 in one month to make 390, the value of x is 500 and the value of y is 390.
when she sells 1000 in one month to make 480, the value of x is 1000 and the value of y is 480.
you have two points that will be on the line of your equation.
they are:
(x1,y1) = 500,390
(x2,y2) = 1000,480
from these two points,you can find the slope.
m is the slope.
m = (x2-x1) / (y2-y1) = (480-390) / (1000-500) = 90/500 = 9/50
your equation becomes y = 9/50 * x + b
to find the y-intercept, replace x and y with the values from one of the points used to find the slope, and solve for b.
i'll use (1000,480).
y = 9/50 * x + b becomes 480 = 9/50 * 1000 + b
solve for b to get b = 480 - 9/50 * 1000
this results in b = 480 - 180 = 300
your equation becomes y = 9/50 * x + 300
any point that's on the line will be modeled by this equaiton.
when x = 2400, the equation becomes y = 9/50 * 2400 + 300.
this results in y = 732.
if she sells 2400 dollars worth of merchandise in a month, she will get paid 732 dollars.
her salary is composed of a flat rate of 300 plus a commission of 432.
the commission part of her salary was equal to 9/50 * 2400.
if you graphed the equation, it would look something like this:
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