Question

How do you write an equation in standard form for a line passing through $\left(3,4\right)$ and $\left(-3,-8\right)$?

Answer 1

Find the equation of a line.

Equation of line passing through the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Given coordinates are $\left(3,4\right)$ and $\left(-3,-8\right)$.

Substituting $3$ for $x_1$, $4$ for $y_1$, $-3$ for $x_2$, $-8$ for $y_2$ in equation $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$, we have

$$\begin{gathered} \Rightarrow y-4=\frac{-8-4}{-3-3}\left(x-3\right) \\ \Rightarrow y-4=\frac{-12}{-6}\left(x-3\right) \\ \Rightarrow y-4=2\left(x-3\right) \\ \Rightarrow y-4=2x-6 \\ \Rightarrow y=2x-6+4\left[\mathrm{Add}\mathrm{both}\mathrm{sides}\mathrm{with}\left(4\right)\right] \\ \therefore y=2x-2 \end{gathered}$$

Hence, the equation of a line passing through the points $\left(3,4\right)$ and $\left(-3,-8\right)$ is $y=2x-2$.