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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
y
=
m
x
through the origin.

(1 point)
Responses

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

y=4x
y
=
4
x
y equals 4 x

y=8x
y
=
8
x
y equals 8 x

y=2x

Answer 1

To derive the equation of the line in the form \( y = mx \), we need to find the slope \( m \) of the line that passes through the points given: \( (2, 4) \), \( (4, 8) \), and \( (5, 10) \).

First, we can find the slope \( m \) using the points. The slope formula between any two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

Let's choose the points \( (2, 4) \) and \( (4, 8) \):

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

This slope \( m = 2 \) can also be confirmed using other pairs of points.

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

\[ y = 2x \]

So the correct response is:

y = 2x