Answer:
y = [tex]-\frac{3}{2}x + 15[/tex]
Step-by-step explanation:
First solve the given equation for y:
-2x + 3y = -6 add 2x to both sides
3y = 2x - 6 divide both sides by 3 to isolate y
y = [tex]\frac{2}{3}x - 2[/tex]
The slope of the given equation (m) is [tex]\frac{2}{3}[/tex], so the slope of a line perpendicular to the given line would be opposite in sign and the reciprocal or m = [tex]-\frac{3}{2}[/tex].
Using the perpendicular slope of m = [tex]-\frac{3}{2}[/tex] and the given point (6,6) plug into the point-slope form of the equation before solving for y:
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex]) Substitute in what you know, [tex]y_{1}[/tex] = 6, [tex]x_{1}[/tex] = 6 and m = [tex]-\frac{3}{2}[/tex]
y - 6 = [tex]-\frac{3}{2}[/tex](x - 6) Now distribute on the right hand side of the equation
y - 6 = [tex]-\frac{3}{2}[/tex]x + 9 Isolate y by adding 6 to both sides
y = [tex]-\frac{3}{2}[/tex]x + 15
