Question
Graphing Linear Equations Online Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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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 2 comma 4 right parenthesis, left parenthesis 4 comma 8 right parenthesis, and left parenthesis 5 comma 10 right parenthesis.
The proportional relationship is shown on the graph. Derive the equation of the line y=mx
through the origin.
(1 point)
Responses
y=12x
y is equal to 1 half x - no response given
y=4x
y is equal to 4 x - no response given
y=8x
y is equal to 8 x - incorrect
y=2x
Answers
GPT-4o mini
To find the equation of the line that passes through the origin and follows the proportional relationship indicated by the points on the graph, we need to determine the slope (m) of the line. We can use any two points from the line given in the task.
From the points provided, let's choose \((2, 4)\) and \((4, 8)\):
1. Calculate the slope (m):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 4}{4 - 2} = \frac{4}{2} = 2
\]
2. The equation of the line in slope-intercept form (y = mx) through the origin is therefore:
\[
y = 2x
\]
Given the response options, the correct answer is:
**y = 2x**.
From the points provided, let's choose \((2, 4)\) and \((4, 8)\):
1. Calculate the slope (m):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 4}{4 - 2} = \frac{4}{2} = 2
\]
2. The equation of the line in slope-intercept form (y = mx) through the origin is therefore:
\[
y = 2x
\]
Given the response options, the correct answer is:
**y = 2x**.