Consider the line 6x+5y=2

what is the slope of a line parallel to this line?

what is the slope of a line perpendicular to this line?

slope of a parallel line:
slope of a perpendicular line:

Step-by-step explanation:

Given

line: 6x + 5y = 2

Step One

Find the line given's slope.

6x + 5y = 2               Subtract 6x from both sides

6x-6x + 5y=2-6x      Combine like terms on the left

5y = 2 - 6x                Divide by 5.

5y/5 = -6x/5 + 2/5    Do the division

y = -(6/5)x     + 2/5

Step Two

Find the parallel slope. Use the number in front of the x

Just read what you have: -6/5

Step Three

Find the perpendicular slope.

Let m1 be the given slope -(6/5)

Let m2 be the perpendicular slope

m1 * m2 = -1

(-6/5) * m2 = - 1           Multiply both sides by 5

(-6/5)*5 * m2 = - 1 * 5  Combine the left 5s cancel.

-6 * m2 = - 5                Divide by - 6

-6 * m2/-6 = -5/-6

m2 = 5/6

Slope of the perpendicular line = 5/6