Answer:
z=-3
Step-by-step explanation:
The given line has slope m=-7.
The line passes through (-1,-8) and (z,6).
We use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=-1[/tex], [tex]y_1=-8[/tex], [tex]x_2=z[/tex] , [tex]y_2=6[/tex] and [tex]m=-7[/tex] to get:
[tex]-7=\frac{6--8}{z--1}[/tex]
[tex]-7=\frac{6+8}{z+1}[/tex]
[tex]-7=\frac{14}{z+1}[/tex]
[tex]-7(z+1)=14[/tex]
Expand [tex]-7z-7=14[/tex]
[tex]-7z=14+7[/tex]
[tex]-7z=21[/tex]
[tex]z=-3[/tex]
