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write an equation in slope intercept form for the line that passes through (6,6) and is perpendicular to "-2x" + 3y =-6

Sagot :

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