Question

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

Answer 1

Equation of the line given as,

$y=mx+c$ ...….$\left(1\right)$

when cm is the slope of the line (i) passing through $(-1,1)$ and $(2,-4)$ is

$m=\frac{1-(-4)}{-1-2}$

$m=\frac{1+4}{-3}$

$m=\frac{-5}{3}$

$\therefore$ equation $\left(1\right)$ becomes

$y=\frac{-5}{3}x+c$ ....$\left(1\right)$

the given line $\left(1\right)$ pass through $(-1,1)$

$\therefore 1=\frac{-5}{3}(-1)+c$

$\Rightarrow 1=\frac{5}{3}+c$

$\Rightarrow c=1-\frac{5}{3}$

$\Rightarrow c=\frac{+3-5}{3}$

$\Rightarrow c=\frac{-2}{3}$

$\therefore$ $\left(1\right)$ becomes

$y=\frac{-5}{3}x-\frac{2}{3}$

$\Rightarrow 3y=-5x-2$

$\Rightarrow 5x+3y+2=0$.