Question

Write the equation of the line y=mx
through the origin that describes the proportional relationship
first point (3, 1) second point (6, 2) third point (9, 3)

Answer 1

To find the equation of the line \( y = mx \) that passes through the origin and describes the proportional relationship based on the given points, we need to determine the slope \( m \).

The points given are:
- \( (3, 1) \)
- \( (6, 2) \)
- \( (9, 3) \)

To find the slope \( m \), we can take any of these points. The formula for the slope is calculated as:

\[
m = \frac{y}{x}
\]

Using the first point \( (3, 1) \):

\[
m = \frac{1}{3}
\]

Using the second point \( (6, 2) \):

\[
m = \frac{2}{6} = \frac{1}{3}
\]

Using the third point \( (9, 3) \):

\[
m = \frac{3}{9} = \frac{1}{3}
\]

Since all points give us the same slope \( m = \frac{1}{3} \), we can write the equation of the line as:

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

This line passes through the origin and accurately represents the proportional relationship established by the given points.