Question

The graph shows the proportional relationship. derive the equation of the line y = mx through the organ

the dots is at 5 and 10

Answer 1

To derive the equation of a line that represents a proportional relationship in the form \(y = mx\), we need to identify the slope \(m\) using the points provided.

You've mentioned that there is a proportional relationship, and indicated a point at (5, 10). In a proportional relationship, the line passes through the origin (0,0) and the format of the equation is indeed \(y = mx\).

1. **Identify the point**: The point given is (5, 10).

2. **Calculate the slope \(m\)**: The slope of a line in a proportional relationship can be calculated using the formula:

\[
m = \frac{y}{x}
\]

Plugging in the coordinates of the point (5, 10):

\[
m = \frac{10}{5} = 2
\]

3. **Write the equation**: Now that we have the slope \(m\), we can write the equation of the line:

\[
y = 2x
\]

Thus, the equation of the line that represents the proportional relationship through the origin and the given point is:

\[
y = 2x
\]