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Antonio works for a car dealership. He's paid a base salary plus a commission for each car he sells. One year Antonio sold 10 cars and made $35,000. Another year he sold 13 cars and made $39,500. Gee, Antonio. Only 23 cars in two whole years? What are you doing, being nice and non-aggressive toward your customers? What kind of a car salesman are you?
What is Antonio's base salary, and what is his per-car commission?
First, we find the linear equation. The amount Antonio is paid depends on how many cars he sells, so let's have
be the number of cars he sells, and
be the amount Antonio gets paid.
We've been told two points on the line: (10, 35,000) and (13, 39,500).
From two points, we can find the slope of the line:
Then we can use one of the points—we'll use (10, 35,000) since the numbers are easier to work with—to build the equation of the line:
Now that we have the equation of the line, figure out what the question is actually asking. We want to find out Antonio's base salary, or the amount Antonio gets paid if he sells 0 cars, also known as the y-intercept of the line. We'll definitely want to know that value, since it seems that Antonio selling 0 cars is pretty much par for the course.
From the equation, we can see that the y-intercept, or Antonio's base salary, is $20,000.
Next, we want to know Antonio's per-car commission. If the number of cars (x) goes up by 1, by how much does Antonio's pay (y) increase? We're really being asked for the slope of the line, which we can see from the equation: 1500. Antonio's per car commission is $1500.
You'd think that sort of money would provide some valuable incentive, but apparently Antonio isn't inspired by money. He must be selling cars because he loves it so much.