Answer
(a) $x=-\frac{1}{15}p+102$
(b) 45 units
(c) 49 units
Work Step by Step
(a) For this problem, we will set up two equations in slope-intercept form. Because the problem denotes x as the dependent variable and p as the independent variable, the general form for the equations is:
$$x=mp+b$$
When rent is \$780, 50 units are occupied. Therefore:
$$50=780m+b$$
When rent is \$825, 47 units are occupied. Therefore:
$$47=825m+b$$
These two equations form a system of equations. We can now solve for m using the elimination method.
$$3=-45m$$
$$m=-\frac{1}{15}$$
Now we can substitute m back into one of the equations and solve for b.
$$50=780(-\frac{1}{15})+b$$
$$50=-52+b$$
$$b=102$$
Therefore:
$$x=-\frac{1}{15}p+102$$
(b) For this problem, you are instructed to use a graphing device. Make sure that the graphing device displays the function at $p=855$. Then, press TRACE and input the value 855. The device should give you the value 45.
Alternatively, you can solve this problem manually by inputting the value $p=855$ for the function.
$$x=-\frac{1}{15}(855)+102$$
$$x=45$$
(c) For this problem, we will input $p=795$ into the equation.
$$x=-\frac{1}{15}(795)+102$$
$$x=49$$
Verify this value by using the TRACE function on a graphing device and inputting the value 795.
