Question

Find an equation of the line passing through the pair of points write the equation in the form AX plus BY equals C(-7,2),(-8,-3)A.x+y=37B. -5x+y=37C.5x+y=-37D.-5x-y=37

Answer 1

Given the points;

$(-7,2),(-8,-3)$

The slope-intercept form of the equation of the line that passes through the pair of points is;

$\begin{gathered} y=mx+c \\ \text{Where m is slope and c is the y-intercept.} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Where;} \\ x_1=-7,y_1=2,x_{2_{}}=-8,y_2=-3 \end{gathered}$$\begin{gathered} m=\frac{-3-2}{-8-(-7)} \\ m=-\frac{5}{-1} \\ m=5 \\ 2=5(-7)+c \\ c=2+35 \\ c=37 \end{gathered}$

Thus, the slope-intercept form of the equation of the line is;

$y=5x+37$

Then, the equation in the form of Ax+By = C is;

$5x-y=-37$

Or we multiply through by -1, we have;

$\begin{gathered} -1(5x-y)=-1(-37) \\ -5x+y=37 \end{gathered}$