Question

Find the equation of the line joining the points $(-1,3)$ and $(4,-2)$.

Answer 1

Solve for equation of line passing through the given points

Given points are $\left(-1,3\right)$ and $\left(4,-2\right)$

$\therefore$ Equation of the line passing through the points $(x_1,y_1)$ and $(x_2,y_2)$ is

$y-y_1=\frac{y_1-y_2}{x_1-x_2}\left(x-x_1\right)$

Substitute the given points in the formula

$\therefore x_1=-1,x_2=4,y_1=3,y_2=-2$

$$\begin{gathered} \Rightarrow y-3=\frac{3-(-2)}{-1-4}\left(x-(-1)\right) \\ \Rightarrow y-3=\frac{3+2}{-1-4}\left(x+1\right) \\ \Rightarrow -5\left(y-3\right)=5(x+1) \\ \Rightarrow -1(y-3)=x+1 \\ \Rightarrow -y+3=x+1 \\ \Rightarrow x+y-2=0 \end{gathered}$$

Hence the required equation of line passing through the points $(-1,3)$ and $(4,-2)$ is $x+y-2=0$