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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 $y=4x$.