James earns a monthly salary of $1200 and a commission of $125 for each car he sells

Question

a. Graph and equation that represents how much James earns in a month in which he sells x cars

Answer 1

Hello, Ava,

Let E be James' monthly earnings, in $/month. We know that he'll earn the base salary of $1200/month, so we can start with:

1) Salary = $1200/month

We also know that he'll each a $125 commission for each car he sells. Let x be the number of cars sold in a month. We can represent the total commissions earned in a month with $125x.

2) Commissions = $125x

Combine these two amounts to find the total earnings, E:

E($/month) = $1200/month + $125x(cars/month)

We can write this in a standard straight line format of y = mx + b

y = 125x + 1200

James' earnings for a month includes a base of 1200 (this is the y-intercept: he doesn't need to sell any cars for the $1200, although I suspect this might be endangered if no cars are sold for a period of time. [This probably needs a limit, e.g., it is only true for longer than a month if x ≥ 5 cars/month] But that's a different class.

The graph will have a label for the y axis of $. The x axis is cars sold in that month. The title of the graph should read "James' Monthly Earnings as a Function of Cars Sold." Pick a range for x that represents the most likely scenarios for cars sold in a month.