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=8x
y equals 8 x

y=2x
y equals 2 x

y=4x
y equals 4 x

y=12x
y equals Start Fraction 1 over 2 End Fraction x
Remaining Attempts : 3
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Answer 1

To find the equation of the line that represents the proportional relationship through the origin, we need to determine the slope (m) based on the given points.

Given points:
- (2, 4)
- (4, 8)
- (5, 10)

We can calculate the slope using one of the points. The slope (m) is defined as the change in y divided by the change in x (rise over run):

Using the points (2, 4) and (4, 8):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 4}{4 - 2} = \frac{4}{2} = 2
\]

Now that we have the slope, we can write the equation of the line in the form \(y = mx\):

\[
y = 2x
\]

So the answer is:

**y = 2x**