Question

Use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?

Answer 1

Neither

Explanation:

The slope of a line is the change in y over change in x:

m = (y₂ − y₁) / (x₂ − x₁)

For Line 1:

m = (-1 − 3) / (4 − 2)

m = -2

For Line 2:

m = (5 − 3) / (8 − 6)

m = 1

If the slopes are equal, the lines are parallel.

If the slopes multiply to -1, the lines are perpendicular.

Otherwise, the lines are neither parallel nor perpendicular.

Here, the slopes are different and do not multiply to -1. So the lines are neither parallel nor perpendicular.

Answer 2

Let's find the slope of line 1

Finding the slope using two points:

The formula for slope is

`(y_(2)-y_(1))/(x_(2)-x_(1))`

In this case...

`y_(2) =-1\\y_(1) =3\\x_(2) =4\\x_(1) =2`

^^^Plug these numbers into the formula for slope...

`(-1 - 3)/(4 - 2)`

`(-4)/(2)`

-2

^^^This is your slope for line 1

Let's find the slope of line 2

In this case...

`y_(2) =5\\y_(1) =3\\x_(2) =8\\x_(1) =6`

^^^Plug these numbers into the formula for slope...

`(5-3)/(8-6)`

`(2)/(2)`

1

^^^This is your slope of line 2

Parallel lines have the same slope. Perpendicular lines have the slope of opposite reciprocal. In this case neither of these are applicable so the answer is...

neither!

Hope this helped!

~Just a girl in love with Shawn Mendes