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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 through the origin that describes the proportional relationship shown in the graph, we need to determine the slope \( m \) of the line passing through the points \( (1, 4) \) and \( (2, 8) \).

First, we can calculate the slope \( m \) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \( (x_1, y_1) = (1, 4) \) and \( (x_2, y_2) = (2, 8) \).

Substituting in the values:

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

Since the equation of the line through the origin is in the form \( y = mx \), we can substitute the value of \( m \):

\[ y = 4x \]

Thus, the equation of the line is \( y = 4x \).