Question

Joshua earns a salary plus a commission for every painting he sells. the equation c= 40p+75, where c is the commission in dollars and p is the number of paintings, represents how much he earns. compare the functions by comparing their y-intercepts and rates of change.

Answer 1

The given function is

$c=40p+75$

Where 40 is the rate of change, and 75 is the y-intercept. This means that Joshua's earnings without the commission are $75, and he earns $40 per painting as commission.

Now, let's find the rate of change of the table

$m=\frac{y_2-y_1}{x_2-x_1}$

Let's replace the points (1, 115) and (2, 150).

$m=\frac{150-115}{2-1}=\frac{35}{1}=35$

So, the rate of change of the table is 35, which means the commission per painting is $35.

Now, we use the point-slope formula to find the equation

$\begin{gathered} y-y_1=m(x-x_1) \\ y-115=35(x-1) \\ y=35x-35+115 \\ y=35x+80 \end{gathered}$

As you can observe, the function shown in the table has 80 as the y-intercept, which means that the earnings without commission are $80.

If we compare, we can say that the first function has greater commission but a lowe salary.