Answer:
y=-37
Step-by-step explanation:
A perpendicular line has a negative reciprocal slope to the original line. We will use the slope formula to find the slope of line m, then take the negative reciprocal for the slope of line n which will reveal the value of y.
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=6\\y_1=8[/tex] and [tex]x_2=-1\\y_2=2[/tex]
[tex]m=\frac{2-8}{-1-6}[/tex]
[tex]m=\frac{2-8}{-1-6}=\frac{-6}{-7} =\frac{6}{7}[/tex]
[tex]m\neq \frac{6}{7}[/tex] for line n because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is [tex]m=-\frac{7}{6}[/tex].
We will substitute [tex]m=-\frac{7}{6}[/tex] into the slope formula to find line n's coordinate value y. We will also substitute [tex]x_1=-1\\y_1=5[/tex] and [tex]x_2=5\\y_2=y[/tex]
.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]-\frac{7}{6}=\frac{y-5}{5-(-1)}[/tex]
[tex]-\frac{7}{6}=\frac{y-5}{6)}[/tex]
[tex]6(-\frac{7}{6})=y-5[/tex]
[tex]-42+5=y-5+5[/tex]
[tex]-37=y[/tex]
