Question

Write the equation of the line y=mx
through the origin that describes the proportional relationship shown in the graph.
POINT ONE:(3,1)
POINT TWO:(6,2)
POINT THREE:(9,3)

Answer 1

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

To find \( m \), we can use any two of the given points. The slope \( m \) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

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

Using these points:

\[
y_1 = 1, \quad x_1 = 3
\]
\[
y_2 = 2, \quad x_2 = 6
\]

Substituting these values into the slope formula:

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

Now, we can write the equation of the line using the slope we found:

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

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

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

This relationship fits with the other points as well:

- For \( x = 9 \):
\[
y = \frac{1}{3} \cdot 9 = 3
\]

So the equation \( y = \frac{1}{3}x \) correctly represents the proportion shown by all the given points.