Question

The graph shows a line and two similar triangles.

On a coordinate plane, a line goes through (0, 2) and (6, 4). A small triangle has a rise of 1 and run of 3 and a larger triangle has a rise of 2 and run of 6.

What is the equation of the line?
y = 3 x
y = one-third x
y = one-third x + 2
y = 3 x + 2

Answer 1

To find the equation of the line that passes through the points (0, 2) and (6, 4), we can first calculate the slope (m) of the line using the formula:

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

Substituting the coordinates of the points (0, 2) and (6, 4):

\[
m = \frac{4 - 2}{6 - 0} = \frac{2}{6} = \frac{1}{3}
\]

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

\[
y - y_1 = m(x - x_1)
\]

Using the point (0, 2):

\[
y - 2 = \frac{1}{3}(x - 0)
\]

This simplifies to:

\[
y - 2 = \frac{1}{3}x
\]
\[
y = \frac{1}{3}x + 2
\]

Thus, the equation of the line is:

\[
y = \frac{1}{3}x + 2
\]

The correct answer is **y = one-third x + 2**.