SOLUTION: Through (-6, 8); perpendicular to 9x + 5y = 66. Write the equation in y = mx + b form. Please show all work.

Algebra ->  Graphs -> SOLUTION: Through (-6, 8); perpendicular to 9x + 5y = 66. Write the equation in y = mx + b form. Please show all work.      Log On


   

Question 1127518: Through (-6, 8); perpendicular to 9x + 5y = 66. Write the equation in y = mx + b form. Please show all work.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
9x+%2B+5y+=+66
slope is -9%2F5


Slope will be 5%2F9 for perpendicular line.

y-8=%285%2F9%29%28x%2B6%29
y=%285%2F9%29%28x%2B6%29%2B8
y=5x%2F9%2B5%2A%282%2F3%29%2B8
y=5x%2F9%2B10%2F3%2B24%2F3
highlight%28y=5x%2F9%2B34%2F3%29

Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


Any line parallel to 9x+5y=66 will have an equation of the form 9x+5y=C, where C is some constant; any line perpendicular to 9x+5y=66 will have an equation of the form 5x-9y=C (switch the coefficients and change the sign of one of them).

So in your problem, an equation of the line you want is 5x-9y=C; the constant C is determined by using the coordinates of the given point.

5(-6)-9(8) = -30-72 = -102

An equation of the line you are looking for is

5x-9y = -102

In slope-intercept form....
9y = 5x+102
y = (5/9)x + 102/9

or

y = (5/9)x + 34/3

If you are supposed to find the solution using basic algebra, then
(1) put the given equation in slope-intercept form to find its slope;
(2) find the slope of the line perpendicular to the given line; and
(3) use the given point to find the y-intercept

(1)...
9x+5y = 66
5y = -9x+66
y = (-9/5)x+66/5

(2)... the perpendicular slope is 5/9, the equation is y=(5/9)x+C

(3)...
8 = (5/9)(-6)+C
8 = -10/3+C
C = 8+10/3 = 34/3

The equation (as found earlier by the other method) is
y = (5/9)x + 34/3