Question 230687
(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( 300, 300, -15, 10, -15, 10, -5x/6 +7/6, 6x/5 -64/5)}}}(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)