Question

Write the equation of the line through the points $(1,–1)\text{and}(3,5)$.

Answer 1

We know that the equation of the line through two points $(x_1,y_1)\&(x_2,y_2)\text{is}y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

So, equation of the line through the points $(1,-1)\text{and}(3,5)$ is
$(y-(-1\left)\right)=\frac{5-(-1)}{3-1}(x-1)$
$\Rightarrow y+1=\frac{5+1}{2}(x-1)$
$\Rightarrow y+1=\frac{6}{2}(x-1)$
$\Rightarrow y+1=3(x-1)$
$\Rightarrow y+1=3x-3$
$\Rightarrow y-3x+1+3=0$
$\Rightarrow y-3x+4=0$

Hence the required equation is
$y-3x+4=0$ or $3x-y-4=0$