Question

Use the image to answer the 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. \( y = 2x \)**