Find an equation of the line that is perpendicular to the line 3x - 5y = 11 and that has the same y-intercept as the line 2x + 9y = 18.

Question

anonymous · Answer

Rearranging the first eqt.:
-5y = 11 - 3x
y = (-11/5) + (3/5)x

The equation of the perpendicular line has a slope of:
          -1/M

If the slope of the line is (3/5) then the perpendicular line will have a slope:
           -1/(3/5) = -5/3

therefore the perpendicular equation is:
           y = (-5/3)x + b

We know that the perpendicular line has the same y-intercept as the line 2x + 9y = 18. To find the y-intercept, x=0:
           0 + 9y = 18
                   y = 2         so,  y-intercepts at (0,2)

Plug in the point into the perpendicular eqt. we find:
           2 = 0 + b
           b = 2

Hence,
y = (-5/3)x + 2


Is that right?