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Question
Use the image to answer the question.

An illustration shows a coordinate plane with 4 quadrants. The x-axis ranges from negative 9 to 9 in one unit increments, and the y-axis ranges from negative 11 to 11 in one unit increments. A line is graphed on the plane. An upward slanting line passes through points plotted at left parenthesis 1 comma 4 right parenthesis and left parenthesis 2 comma 8 right parenthesis.

Find the equation of the line y=mx
through the origin that describes the proportional relationship shown in the graph.

(1 point)

Answer 1

To find the equation of the line that describes the proportional relationship through the origin (0,0), we need to determine the slope of the line that passes through the points (1, 4) and (2, 8).

1. First, we calculate the slope (m) using the formula:

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

Here, (x1, y1) = (1, 4) and (x2, y2) = (2, 8).

\[
m = \frac{8 - 4}{2 - 1} = \frac{4}{1} = 4
\]

2. Since we are finding the equation of the line that goes through the origin, the equation will take the form of:

\[
y = mx
\]

Substituting the slope we found:

\[
y = 4x
\]

Therefore, the equation of the line that describes the proportional relationship is:

\[
y = 4x
\]