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

1 answer

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.