Graph the line through the points (-6,4) and (6,-8):
(a) when x = -6 , y = 4 and x = 6 , y = -8
(b) Write an equation of a line in the form y = mx+b
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ (-6,4)\longrightarrow x_1=-6,y_1=4 \\ (6,-8)\longrightarrow x_2=6,y_2=-8 \end{gathered}[/tex][tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \frac{y-4}{x--6_{}}=\frac{-8-4}{6--6} \\ \frac{y-4}{x+6}=-\frac{12}{6+6} \\ \frac{y-4}{x+6}=-\frac{12}{12} \\ \frac{y-4}{x+6}=-1 \\ \text{cross multiply} \\ y-4=-1(x+6) \\ y-4=-x-6 \\ \text{add 4 to both side } \\ y-4+4=-x-6+4 \\ y=-x-2 \end{gathered}[/tex]Therefore the equation of the line is y = -x -2
