Question

Find the equation of the line which is passing through the points $(-1,1)$ and $(2,-4)$.

Answer 1

We know that equation of line through two points $(x_1,y_1)$ and $(x_2,y_2)$ is
$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$
So, equation of the line through the points $(-1,1)$ and $(2,-4)$ is
$(y-1)=\frac{-4-1}{2-(-1)}(x-(-1\left)\right)$
$\Rightarrow (y-1)=\frac{-5}{2+1}(x+1)$
$\Rightarrow (y-1)=\frac{-5}{3}(x+1)$
$\Rightarrow 3(y-1)=-5(x+1)$
$\Rightarrow 3y-3=-5x-5$
$\Rightarrow 5x+3y+2=0$
Hence, the required equation is $5x+3y+2=0$