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 3 comma 1 right parenthesis, left parenthesis 6 comma 2 right parenthesis, and left parenthesis 9 comma 3 right parenthesis.

Write the equation of the line y=mx
through the origin that describes the proportional relationship shown in the graph. Express your answer as a fraction in simplified form.

(1 point)
y=
Remaining Attempts : 3
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Answer 1

GPT-4o mini wrong

Answer 2

To determine the equation of the line that passes through the origin and is proportional to the points on the line given, we can find the slope \( m \) of the line.

Given two points from the set of points that the line passes through, let's use the points \( (3, 1) \) and \( (6, 2) \) to calculate the slope:

The formula for the slope \( m \) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using points \( (3, 1) \) and \( (6, 2) \):

\[
m = \frac{2 - 1}{6 - 3} = \frac{1}{3}
\]

Now that we have the slope, we can write the equation of the line that passes through the origin \( (0,0) \):

\[
y = mx
\]

Substituting the slope \( m = \frac{1}{3} \):

\[
y = \frac{1}{3}x
\]

Therefore, the equation of the line in slope-intercept form is:

\[
\boxed{\frac{1}{3}x}
\]

Thus, expressing it simply as \( y = \frac{1}{3}x \), we can write:

\[
y = \frac{1}{3}
\]

as the final answer.