Question

The graph
dot One (2, 10)
2 (1,5)

The graph shows the propositional relationship. Derive the equation of the line y = mx through the origin.

Answer 1

To derive the equation of the line that goes through the origin and the points (2, 10) and (1, 5), we can follow these steps:

1. **Find the slope (m)**: The slope (m) of a line that goes through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

Let's use the points (2, 10) and (1, 5):

- \((x_1, y_1) = (1, 5)\)
- \((x_2, y_2) = (2, 10)\)

Plug in the values:

\[
m = \frac{10 - 5}{2 - 1} = \frac{5}{1} = 5
\]

2. **Write the equation of the line**: Since we want the line through the origin (0, 0) with slope \(m\), the equation of the line can be expressed as:

\[
y = mx
\]

Substituting the calculated slope:

\[
y = 5x
\]

Therefore, the equation of the line passing through the origin with respect to the points given is:

\[
y = 5x
\]