Question

Find the slope of the line that is parallel and perpendicular to the following equation.

2x-2y=-6

Answer 1

Parallel lines 1

perpendicular lines -1

Explanation:

2x-2y = -6

Solve for y to get it in slope intercept form

-2y = -2x-6

Divide by -2

y = x+3

This is slope intercept form y = mx+b where m is the slope

Parallel lines have the same slope

A parallel line would have a slope of 1

Perpendicular lines would have a slope that is a negative reciprocal

-1/1

Perpendicular lines would have a slope of -1

Answer 2

Let us first put it into slope-intercept form ⇒
`y = mx + b`

• m: slope
• b: y-intercept of the function

To put it into that format, we need to simply put y on one side of the equation and the rest on the other side

`2x - 2y =-6\\-2y = -2x -6\\y = x +3`

What do we want to find first ⇒ a line parallel to the original line

• a line that is parallel to the original line only has one requirement, it must have the same slope, such as the one below

`y = x +5`

What do we also want to find ⇒ a line perpendicular to the original line

• a line that is perpendicular to the original line only has one requirement, the slope has to be the negative reciprocal of the original slope

⇒ original slope is 1 ⇒ negative reciprocal is - 1/1 = -1

⇒ so an example is

`y = -x + 3`

Answer:

• Line that is parallel: slope is 1
• Line that is perpendicular: slope is -1

Hope that helps!