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)
Remaining Attempts : 3
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Answer 1

To find the equation of the line that passes through the origin (0,0) and has the same slope as the line described, we can follow these steps:

1. **Determine the slope (m)**: The slope of a line (m) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where (x1, y1) and (x2, y2) are two points on the line.

From the points (1, 4) and (2, 8):
- \( y_1 = 4, y_2 = 8, x_1 = 1, x_2 = 2 \)

Plugging in these values:
\[
m = \frac{8 - 4}{2 - 1} = \frac{4}{1} = 4
\]

2. **Write the equation**: The equation of a line that passes through the origin is given by:
\[
y = mx
\]
Substituting the slope (m = 4):
\[
y = 4x
\]

Thus, the equation of the line through the origin that describes the proportional relationship shown in the graph is:
\[
\boxed{y = 4x}
\]