Question

the graph represents revenue in dollars as a function of greeting cards sold. greeting card revenue (graph with x-axis number of cards sold from 0 to 10, y-axis revenue ($) from 0 to 20, line passing through origin and (5,20) approximately) which equation represents the function shown on the graph? \\( y = \frac{1}{4}x \\) \\( y = \frac{1}{2}x \\) \\( y = 2x \\) \\( y = 4x \\)

Explanation:

Step1: Identify two points on the line

From the graph, when \( x = 2 \) (number of cards sold), \( y = 8 \) (revenue in dollars). Another point is \( x = 0 \), \( y = 0 \) (since it passes through the origin).

Step2: Calculate the slope \( m \)

The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using \( (0,0) \) and \( (2,8) \), we get \( m=\frac{8 - 0}{2 - 0}=\frac{8}{2}=4 \).

Step3: Determine the equation

Since the line passes through the origin, the equation is in the form \( y = mx \), where \( m = 4 \). So the equation is \( y = 4x \).

Answer:

\( y = 4x \) (the option: \( y = 4x \))