Question

tyler is a salesperson who sells computers at an electronics store. he makes a base pay amount each day and then is paid a commission for every computer sale he makes. let $p$ represent tylers total pay on a day on which he sells $x$ computers. a graph of $p$ is shown below. write an equation for $p$ then state the $y$-intercept of the graph and determine its interpretation in the context of the problem.
note: the line drawn is dotted because the domain of the function is limited to the integers.
answer attempt 1 out of 2
$p =$
the $y$-intercept of the function is which represents

Explanation:

Step1: Find the slope

The line passes through $(0,60)$ and $(10,75)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{75 - 60}{10-0}=\frac{15}{10}=1.5$.

Step2: Write the equation

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. Since $m = 1.5$ and $b = 60$ (the value of $y$ when $x = 0$), the equation for $P$ is $P=1.5x + 60$.

Step3: Identify the $y$-intercept

The $y$-intercept is the value of $P$ when $x = 0$. From the graph and the equation, when $x = 0$, $P = 60$. In the context of the problem, when Tyler sells $0$ computers ($x = 0$), his pay is $60$ dollars, so $60$ represents his base - pay amount each day.

Answer:

$P = 1.5x+60$; The $y$-intercept of the function is $60$ which represents Tyler's base - pay amount each day.