Use the image to answer the question.

Question

An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line passes through points plotted at left parenthesis 3 comma 1 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 9 comma 3 right parenthesis.

Write the equation of the line y=mx
through the origin that describes the proportional relationship shown in the graph.

page 14 of 16

Answer 1

To find the equation of the line in the form \( y = mx \) that describes the proportional relationship, we need to determine the slope \( m \) using the two points provided on the line.

Let's use the points \( (3, 1) \) and \( (6, 2) \).

1. Calculate the slope \( m \):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 1}{6 - 3} = \frac{1}{3} \]

2. Now that we have the slope, we can write the equation of the line in the form \( y = mx \):

\[ y = \frac{1}{3}x \]

Thus, the equation of the line that describes the proportional relationship is:

\[ y = \frac{1}{3}x \]