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

it would be 5/2 because it goes up five and over 2