SOLUTION: Write the equation of the line containing the given point and perpendicular to the given line. (4,-8): 5x + 6y = 7

Algebra ->  Linear-equations -> SOLUTION: Write the equation of the line containing the given point and perpendicular to the given line. (4,-8): 5x + 6y = 7      Log On


   

Question 230687: Write the equation of the line containing the given point and perpendicular to the given line.
(4,-8): 5x + 6y = 7
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(4,-8):
5x + 6y = 7
6y=-5x+7
y=-5x/6+7/6 This line has a slope=-5/6 a perpendicular line will have a slope=6/5 (the negative reciprical). (red line)
-8=6/5*4+b
-8=24/5+b
b=-8-24/5
b=(-8*5-24)/5
b=-40-24/5
b=-64/5 the y intercept.
y=6x/5-64/5(green line)
+graph%28+300%2C+300%2C+-15%2C+10%2C+-15%2C+10%2C+-5x%2F6+%2B7%2F6%2C+6x%2F5+-64%2F5%29(graph 300x300 pixels, x from -15 to 10, y from -15 to 10, of TWO functions -5x/6 +7/6 and 6x/5 -64/5).
-5x/6+7/6=6x/5-64/5
(-5x+7)/6=(6x-64)/5
5(-5x+7)=6(6x-64)
-25x+35=36x-384
-25x-36x=-384-35
-61x=-419
x=-419/-61
x=6.869 ans.
y=6*6.869/5-64/5
y=41.214/5-64/5
y=-22.786/5
y=-4.557 ans.
(6.869,-4.557)