(10, 5)

Question

(8, 4)
(4, 2)

The proportional relationship is shown on the graph. Derive the equation of the line y = mx through the origin.

A. y = 4x
B. y = 1/2x
C. y = 2x
D. y = 8x

Answer 1

To find the equation of a proportional relationship that passes through the origin, we can determine the slope \( m \) using the given points.

Using point \( (10, 5) \): \[ m = \frac{y}{x} = \frac{5}{10} = \frac{1}{2} \]

Using point \( (8, 4) \): \[ m = \frac{y}{x} = \frac{4}{8} = \frac{1}{2} \]

Using point \( (4, 2) \): \[ m = \frac{y}{x} = \frac{2}{4} = \frac{1}{2} \]

In all cases, we find that \( m = \frac{1}{2} \). Thus, the equation of the line in slope-intercept form is: \[ y = \frac{1}{2}x \]

So, the correct answer is: B. y = \frac{1}{2}x