Find an equation of the line through the pair of points. Write the equation in the form Ax + By = C.
-$( 4 , - 8 )$ and $( 0 , - 5 )$
A) $12 x + 5 y = - 25$
B) $- 3 x + 4 y = - 20$
C) $- 12 x - 5 y = - 25$
D) $3 x + 4 y = - 20$

Question

Quizplus · Accepted Answer

First, find the slope $m$ of the line passing through the points $(4, -8)$ and $(0, -5)$ using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. This gives $m = \frac{-5 - (-8)}{0 - 4} = \frac{3}{-4} = -\frac{3}{4}$. Then, use point-slope form $y - y_1 = m(x - x_1)$ with one of the points, say $(4, -8)$, to get $y + 8 = -\frac{3}{4}(x - 4)$. Simplifying and converting to $Ax + By = C$ form gives $3x + 4y = -20$.

Find an Equation of the Line Through the Pair of Points