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.
1 answer