# Find the equation of the line which passes through the points

Question:

Find the equation of the line which passes through the points (–1, 1) and (2, –4).

Solution:

It is known that the equation of the line passing through points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is $y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\left(x-x_{1}\right)$.

Therefore, the equation of the line passing through the points (–1, 1) and

(2, –4) is

$(y-1)=\frac{-4-1}{2+1}(x+1)$

$(y-1)=\frac{-5}{3}(x+1)$

$3(y-1)=-5(x+1)$

$3 y-3=-5 x-5$

i.e., $5 x+3 y+2=0$