Question

popcorn a movie theater sells popcorn in a reusable bucket for $3.50. they offer refills for $2.50 each. plot a line to model the cost in dollars, y, for x refills

Explanation:

Step1: Define the cost function

The initial cost of the bucket is $3.50, and each refill costs $2.50. So the cost function is $y = 2.5x + 3.5$, where $x$ is the number of refills and $y$ is the total cost.

Step2: Find two points to plot

• When $x = 0$ (no refills), $y = 2.5(0)+3.5 = 3.5$. So the point is $(0, 3.5)$.
• When $x = 1$ (one refill), $y = 2.5(1)+3.5 = 6$. So the point is $(1, 6)$.
• When $x = 2$ (two refills), $y = 2.5(2)+3.5 = 8.5$. So the point is $(2, 8.5)$.
• When $x = 3$ (three refills), $y = 2.5(3)+3.5 = 11$. But looking at the y - axis (up to 10), we can use $(0, 3.5)$ and $(1, 6)$ or $(2, 8.5)$ (since 8.5 is less than 10).

To plot the line, we can use the points $(0, 3.5)$ and $(2, 8.5)$ (or other valid points from the function). First, locate $(0, 3.5)$ on the coordinate plane (x = 0, y = 3.5) and $(2, 8.5)$ (x = 2, y = 8.5), then draw a straight line through these points.

Answer:

The cost function is $y = 2.5x + 3.5$. To plot the line, use points like $(0, 3.5)$ and $(2, 8.5)$ (or other points from the function) and draw a straight line through them.