Question

Write the equation of the line through the points $(1,-1)$ and $(3,5)$.

Answer 1

Equation of line through points $(1,-1)$ and $(3,5)$ is

$y=mx+c$

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{5+1}{3-1}=3$

Now equation of line is

$y=3x+c....\left(1\right)$

amd $(1,-1)$ satisfy this equation so

$-1=3+c$ $\Rightarrow$ $[c=-4)$

from equation (1)

$y=3x-4$