Question

Find the equation of the line passing through the points $(-2,-3)$ and $(-4,7)$

Answer 1

Let $A=(-2,-3)=(x_1,y_1)$
$B=(-4,7)=(x_2,y_2)$
Equation of a line in two point form is
$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$
$\Rightarrow y+3=\frac{7+3}{-4+2}(x+2)$
$\Rightarrow y+3=-5(x+2)$
$\Rightarrow y+3=-5x-10$
$\therefore 5x+y+13=0$ is the required equation.