Question

find the equation is standard form, of the line passing through he points (2,-3) and (4,2)

Answer 1

The point slope formula:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

$(2,\ -3)\to x_1=2,\ y_1=-3\\(4,\ 2)\to x_2=4,\ y_2=2$

Substitute:

$m=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}=2.5\\\\y-(-3)=2.5(x-2)\\\\y+3=2.5x-5\ \ \ \ |+5\\\\y+8=2.5x\ \ \ \ \ \ |-y\\\\2.5x-y=8\ \ \ \ \ |\cdot2\\\\\boxed{5x-2y=16}$