The graph

Question

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:

$$y=5x$$