Question

The graph shows a line and two similar triangles.

On a coordinate plane, a line goes through (0, 0) and (6, 4). A small triangle has a rise of 2 and run of 3. A larger triangle has a rise of 4 and run of 6.

What is the equation of the line?
y = three-halves x
y = two-thirds x
y = 3 x
y = 2 x

Answer 1

To find the equation of the line, we can first determine the slope of the line using the two points it passes through: (0, 0) and (6, 4).

The formula for the slope \( m \) is given by:

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

Using the points (0,0) as \((x_1, y_1)\) and (6, 4) as \((x_2, y_2)\):

\[
m = \frac{4 - 0}{6 - 0} = \frac{4}{6} = \frac{2}{3}
\]

Now that we have the slope, we can use the slope-intercept form of a line, which is:

\[
y = mx + b
\]

Since the line passes through the origin (0, 0), the y-intercept \( b \) is 0. Thus, the equation simplifies to:

\[
y = \frac{2}{3}x
\]

Therefore, the equation of the line is:

\[
\boxed{y = \frac{2}{3}x}
\]