Question

Write the equation of the line that is perpendicular to the line 2x − 3y = 3 and passes through the point (−8, 2).

Answer 1

The slope of the given line is
\[
m=\frac 2 3
\]

Answer 2

The line perpendicular to is has an equation\[
y= -\frac 32 x +b
\]

Answer 3

Find b so the line passes through (-8,2)

Answer 4

\[
2 = -\frac 3 2 (-8) + b\\
2= 12 + b\\
b=-10
\]

Answer 5

The equation is
\[
y= -\frac 3 2 x -10
\]