Question

Use the image to answer the question.



The graph shows the proportional relationship. Derive the equation of the line y=mx
𝑦
=
𝑚
𝑥
through the origin.

(1 point)

Answer 1

To derive the equation of the line in the form \( y = mx \) where \( m \) is the slope, you need to identify the slope \( m \) from the graph.

1. **Identify two points on the line:** Look for coordinates of two clear points on the line. For example, if the line passes through (1, 2) and (3, 6).

2. **Calculate the slope \( m \):** The slope is given by the formula:
\[
m = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the example points:
\[
m = \frac{6 - 2}{3 - 1} = \frac{4}{2} = 2
\]

3. **Write the equation:** Plug the value of \( m \) into the equation \( y = mx \):
\[
y = 2x
\]

If you have the specific points or slope from the graph, simply follow these steps with that data to find the equation of the line. If you need the calculation for different specific points, please provide those points for accurate results.