Question

write the equation of the line y=mx through the origin that describes the proportional relationship shown in the graph.
3, 6, 9

Answer 1

To find the equation of the line \( y = mx \) that describes the proportional relationship given by the points (1, 3), (2, 6), and (3, 9), we need to determine the slope \( m \).

Since the relationship is proportional, we can calculate \( m \) using any of the points. The slope \( m \) is defined as:

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

Using the points provided:

1. Using the point (1, 3):
\[
m = \frac{3}{1} = 3
\]

2. Using the point (2, 6):
\[
m = \frac{6}{2} = 3
\]

3. Using the point (3, 9):
\[
m = \frac{9}{3} = 3
\]

In each case, we find that \( m = 3 \).

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

\[
y = 3x
\]