Question

The graph shows a line and two similar triangles.

On a coordinate plane, a line goes through (0, 0) and (8, 2). A small triangle has a rise of 1 and run of 4, and a larger triangle has a rise of 2 and run of 8.

Which expression finds the equation of the line?
StartFraction y Over x EndFraction = one-fourth
StartFraction y Over 4 EndFraction = StartFraction x Over 1 EndFraction
StartFraction y Over x EndFraction = StartFraction 4 Over 1 EndFraction
StartFraction y Over 1 EndFraction = StartFraction 4 Over x EndFraction

Answer 1

To find the equation of the line that passes through the points (0, 0) and (8, 2), we first determine the slope of the line. The slope (m) can be calculated using the formula:

\[
m = \frac{\text{rise}}{\text{run}} = \frac{2 - 0}{8 - 0} = \frac{2}{8} = \frac{1}{4}
\]

The slope of the line is \( \frac{1}{4} \). The equation of the line in slope-intercept form is:

\[
y = mx + b
\]

Since the line passes through the origin (0, 0), the y-intercept \( b = 0 \). Therefore, the equation of the line is:

\[
y = \frac{1}{4}x
\]

To express this in terms of the given options, we can rewrite this equation as follows:

\[
\frac{y}{x} = \frac{1}{4}
\]

Thus, the correct expression that finds the equation of the line is:

\[
\frac{y}{x} = \frac{1}{4}
\]

So the answer is:

**StartFraction y Over x EndFraction = one-fourth**