```Question 389511
(-9,6)_2x=3y+8

Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
3y+8=2x

Since 8 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 8 from both sides.
3y=-8+2x

Move all terms not containing y to the right-hand side of the equation.
3y=2x-8

Divide each term in the equation by 3.
(3y)/(3)=(2x)/(3)-(8)/(3)

Simplify the left-hand side of the equation by canceling the common factors.
y=(2x)/(3)-(8)/(3)

To find the slope and y intercept, use the y=mx+b formula where m=slope and b is the y intercept.
y=mx+b

Using the y=mx+b formula, m=(2)/(3).
m=(2)/(3)

The negative reciprocal of <Z>I<z> is 0.
mperp=-(3)/(2)

Find the equation of the perpendicular line using the point-slope formula.
(-9,6)_m=-(3)/(2)

Find the value of b using the formula for the equation of a line.
y=mx+b

Substitute the value of m into the equation.
y=(-(3)/(2))*x+b

Substitute the value of x into the equation.
y=(-(3)/(2))*(-9)+b

Substitute the value of y into the equation.
(6)=(-(3)/(2))*(-9)+b

Since b is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
(-(3)/(2))*(-9)+b=(6)

Multiply (-(3)/(2)) by (-9) to get (-(3)/(2))(-9).
(-(3)/(2))(-9)+b=(6)

Remove the parentheses around the expression 6.
(-(3)/(2))(-9)+b=6

Multiply -(3)/(2) by -9 to get (27)/(2).
((27)/(2))+b=6

Reorder the polynomial (27)/(2)+b alphabetically from left to right, starting with the highest order term.
b+(27)/(2)=6

Find the value of b.
b=-(15)/(2)

Now that the values of m(slope) and b(y-intercept) are known, substitute them into y=mx+b to find the equation of the line.
y=-(3x)/(2)-(15)/(2)```