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