Question

5 there are two payment options for downloading movies from a web site

• option a: pay $30 for a membership and $2 per movie downloaded
• option b: shown on the grid to the right

option a would have an equation of
y = 2x + 30
option b would have an equation of
y = 5x
ic2 a) graph option a on the grid to the right.
ic1 b) complete the statement below
at both places, the cost of
downloading ____ movies
is $____
ia3 c) verify the coordinates of the point of intersection algebraically by using the substitution method.
\\( \

$$\begin{cases} y = 2x + 30 \\\\ y = 5x \\end{cases}$$

\\)

Explanation:

Part (b)

Step1: Find intersection of equations

To find when the costs are equal, set \( y = 2x + 30 \) and \( y = 5x \) equal:
\( 5x = 2x + 30 \)

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides:
\( 5x - 2x = 30 \)
\( 3x = 30 \)
Divide by 3:
\( x = 10 \)

Step3: Find \( y \) (cost)

Substitute \( x = 10 \) into \( y = 5x \):
\( y = 5(10) = 50 \)

Part (c)

Step1: Substitute \( y = 5x \) into \( y = 2x + 30 \)

Since both equal \( y \), replace \( y \) in \( y = 2x + 30 \) with \( 5x \):
\( 5x = 2x + 30 \)

Step2: Solve for \( x \)

Subtract \( 2x \): \( 3x = 30 \) → \( x = 10 \)

Step3: Find \( y \)

Substitute \( x = 10 \) into \( y = 5x \): \( y = 5(10) = 50 \)

Answer:

(Part b):
At both places, the cost of downloading \(\boldsymbol{10}\) movies is \(\boldsymbol{\$50}\).