Question

The line passing through the origin and the point ($-$3, 5)

Answer 1

The equation of line passing through the origin i.e. (0, 0) and the point ($-$3, 5) using the equation in two point form is

$$\begin{gathered} \frac{x-x_1}{x_1-x_2}=\frac{y-y_1}{y_1-y_2} \\ \Rightarrow \frac{x-0}{0-\left(-3\right)}=\frac{y-0}{0-5} \\ \Rightarrow \frac{x}{3}=\frac{y}{-5} \\ \Rightarrow -5x=3y \\ \Rightarrow 5x+3y=0 \end{gathered}$$