Question

skylar is a salesperson who sells computers at an electronics store. she makes a base pay amount each day and then is paid a commission for every computer sale she makes. let \\(p\\) represent skylars total pay on a day on which she 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.

answer:
\\(p = \\)

the \\(y\\)-intercept of the function is \\(\quad\\) which represents

• the number of computers skylar sold in a day
• the total pay skylar makes each day
• the base pay skylar makes regardless of computer sales
• the commission skylar makes for each computer sale

Explanation:

Identify the y-intercept

The vertical axis represents Skylar's Daily Pay in Dollars \(P\), and the horizontal axis represents the Number of Computers Sold \(x\).
Looking at the graph, the line crosses the vertical axis (\(y\)-axis) at \(P = 50\).
Therefore, the \(y\)-intercept is \(50\).

Determine the slope

We need to find another clear point on the grid to calculate the slope \(m\).
Looking closely at the grid:
At \(x = 0\), \(P = 50\).
At \(x = 4\), \(P = 70\).
At \(x = 8\), \(P = 90\).
Using the points \((0, 50)\) and \((4, 70)\):

$$m = \frac{70 - 50}{4 - 0} = \frac{20}{4} = 5$$

Write the equation

Using the slope-intercept form \(P = mx + b\):

$$P = 5x + 50$$

Interpret the y-intercept

The \(y\)-intercept occurs when \(x = 0\) (no computers are sold).
At \(x = 0\), \(P = 50\), which is the base pay Skylar makes each day regardless of sales.
From the dropdown options:

• "the number of computers Skylar sold in a day"
• "the total pay Skylar makes each day"
• "the base pay Skylar makes regardless of computer sales"
• "the commission Skylar makes for each computer sale"

The correct interpretation is "the base pay Skylar makes regardless of computer sales".

Answer:

\(P =\) <blank>\(5x + 50\)</blank>

The \(y\)-intercept of the function is <blank>\(50\)</blank> which represents <blank>the base pay Skylar makes regardless of computer sales</blank>