Question

Which of the following is the equation of a line that passes through (-2,1) and (-4,-3)?

Answer 1

Points $X(-2,1)$ and $(-4,-3)$ are defined therefore we have all data we need to construct equation.

Linear function has a form of,

$y=ax+b$

First calculate the slope a.

$a=\dfrac{dy}{dx}=\dfrac{-3-1}{-4-1}=\dfrac{-4}{-5}=\dfrac{4}{5}$

Now plug in the coordinates of either one of the points into the linear function. I'll pick point X.

$y=ax+b\Longrightarrow1=\dfrac{4}{5}\cdot(-2)+b$

Now just solve for b.

$1=-\dfrac{8}{5}+b\Longrightarrow b=\dfrac{13}{5}$

The equation is therefore,

$\boxed{y=\dfrac{4}{5}x+\dfrac{13}{5}}$

Hope this helps.

r3t40