Question

What is the slope of a line that is perpendicular to 6x + 3y = –9?

Answer 1

slope of a line ax+by+c=0 is
m=-a/b
in this case a=6, b=3
m1= -6/3= -2

Answer 2

slope of a line which is perpendicular to above line m2
m1 * m2 =-1
(-2) * m2 =-1
m2= -1/-2
m2 = 1/2

Answer 3

You have to change 6x+2y=-9 to y=mx+b where m would be your slope that you can base on for your perpendicular slope.

So, algebra:
1) subtract 6x from both sides
2y=-6x-9
2) divide two on both sides
y=-6/2x-9/2
3) simplify
y=-3x-9/2

Your slope is -3x. A perpendicular slope is the negative reciprocal of your given slope -3x which is 1/3x.

1/3x is your perpendicular slope. If you have questions on how I got to the answer, please reply! I hope I helped!