Use the image to answer the question.

Question

(5, 10), (4, 8), (2, 4)
The proportional relationship is shown on the graph. Derive the equation of the line y = mx through the origin.
A. y = 4x
B. y = 2x
C. y = 8x
D. y = 1/2x

Answer 1

To find the equation of the line \( y = mx \) that goes through the origin based on the given points \((5, 10)\), \((4, 8)\), and \((2, 4)\), we need to determine the slope \( m \).

The slope \( m \) can be found by using any two points. Let's take the points \((2, 4)\) and \((4, 8)\):

1. Calculate the difference in the y-values: \[ 8 - 4 = 4 \]

2. Calculate the difference in the x-values: \[ 4 - 2 = 2 \]

3. Now, compute the slope \( m \): \[ m = \frac{\text{change in } y}{\text{change in } x} = \frac{4}{2} = 2 \]

Therefore, the equation of the line is: \[ y = 2x \]

Thus, the correct answer is: B. \( y = 2x \)