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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 5 right parenthesis and left parenthesis 2 comma 10 right parenthesis.

The graph shows the proportional relationship. Derive the equation of the line y=mx through the origin.

(1 point)
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Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the equation of the line through the origin, we need to find the slope of the line passing through the points (1,5) and (2,10).

First, we find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
m = (10 - 5) / (2 - 1)
m = 5 / 1
m = 5

Now that we have the slope, we can write the equation of the line in slope-intercept form: y = mx + b

Since the line passes through the origin (0,0), we know that the y-intercept (b) is 0. So the equation of the line is:
y = 5x

Therefore, the equation of the line through the origin is y = 5x.