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
Mark this and return

Answer 1

To find the equation of the line that passes through the points (0, 0) and (8, 2), we can start by calculating the slope of the line.

The slope (\(m\)) is calculated as follows:

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

Since the line passes through the origin (0, 0), the equation of the line can be written in slope-intercept form (\(y = mx + b\)), where \(b\) is the y-intercept. In this case, \(b = 0\), so the equation simplifies to:

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

To find which of the provided expressions matches this equation, we can rewrite it in a suitable form:

1. Start with \(y = \frac{1}{4}x\).

To express it as a fraction:

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

This matches the first option:

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

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

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