A graph shows a positive slope with four plot points

Question

Dot 1: (2, 4)
Dot 2: (4, 8)
Dot 3: (5, 10)
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=12x
y equals Start Fraction 1 over 2 End Fraction x

y=4x
y equals 4 x

y=2x

Answer 1

To find the equation of the line \(y = mx\) that passes through the origin and is proportional to the given points, we need to determine the slope \(m\) from the points.

We can use any two points to calculate the slope \(m\). Let's use Dot 1 \((2, 4)\) and Dot 2 \((4, 8)\).

The slope \(m\) is calculated as follows:

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

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

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

Thus, the equation of the line is:

\[ y = 2x \]

The correct response is:

y = 2x