We have the following:
The equation in slope and y-intercept form is as follows
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
we can calculate the slope of the perpendicular line with the following formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}_{}[/tex]replacing:
[tex]m=\frac{7-1}{6-(-2)}=\frac{6}{6+2}=\frac{6}{8}=\frac{3\cdot2}{4\cdot2}=\frac{3}{4}[/tex]The slope is 3/4 .
When two lines are perpendicular, the slopes are opposite, therefore we can calculate the other slope like this
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ \\ \frac{3}{4}\cdot m_2=-1 \\ m_2=-\frac{4}{3} \end{gathered}[/tex]The slope is -4/3, for b, x = - 6 and y = 9, replacing in the equation of the beginning
[tex]\begin{gathered} 9=-\frac{4}{3}\cdot-6+b \\ 9=8+b \\ b=9-8 \\ b=1 \end{gathered}[/tex]The equation is:
[tex]y=-\frac{4}{3}x+1[/tex]