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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=4x
y equals 4 x

y=8x
y equals 8 x

y=12x
y equals Start Fraction 1 over 2 End Fraction x

y=2x
y equals 2 x
Remaining Attempt

1 answer

To find the equation of the line \( y = mx \) that passes through the origin and describes the proportional relationship depicted in the graph, we need to determine the slope \( m \).

We can use any two points that the line passes through. Let's use the points \( (2, 4) \) and \( (4, 8) \).

  1. Calculate the slope \( m \) using the formula:

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

Using the points \( (x_1, y_1) = (2, 4) \) and \( (x_2, y_2) = (4, 8) \):

\[ m = \frac{8 - 4}{4 - 2} = \frac{4}{2} = 2 \]

  1. Therefore, the equation of the line is:

\[ y = 2x \]

So the correct response is:

y=2x