Question

what equation presents the line that passes through the points (-3, 7) and (9,-1).

Answer 1

Consider that the equation of a straight line passing through two points is given by,

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

The points are given as,

$\begin{gathered} (x_1,y_1)=(-3,7) \\ (x_2,y_2)=(9,-1) \end{gathered}$

So the equation of line passing through these points is given by,

$\begin{gathered} y-7=\frac{(-1)-7_{}}{9-(-3)}(x-(-3)) \\ y-7=\frac{-1-7}{9+3}(x+3) \\ y-7=\frac{-8}{12}(x+3) \\ y-7=\frac{-2}{3}(x+3) \\ 3y-21=-2x-6 \\ 2x+3y-21+6=0 \\ 2x+3y-15=0 \end{gathered}$

Thus, the equation of the line passing through the given points is 2x + 3y - 15 = 0 .