Question

Graphing Linear Equations Unit Test

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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 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 in the form y = mx through the origin, we need to calculate the slope (m) using the two points given: (1, 5) and (2, 10).

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

So, the slope of the line is 5.

Now, plug the slope into the equation y = mx:
y = 5x

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