Question

Is y=-3/4×+2 and 3x-4y=-8 parallel,perpendicular,or neither.
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Answer 1

Answer: neither

Explanation:

Two lines are said to be parallel if the have the same slope

Two lines are said to be perpendicular if the product of the slope of the two lines = 1 , that is if
`m_(1)` is the slope of the first line and
`m_(2)` is the slope of the second line , then

`m_(1)` x
`m_(2)` = -1

`m_(1)` = -1/
`m_(2)`

The given lines are

y = -3/4 x + 2 and 3x - 4y = -8

Let us write the two lines in slope - intercept form , that is in the form

y = mx + c , where m is the slope and c is the y - intercept.

The first line is already in this form , this means that
`m_(1)` = -3/4

To find
`m_(2)` , we must first of all write the equation in slope - intercept form , that is , we will make y the subject of the formula

3x - 4y = -8

4y = 3x + 8

y = 3/4x + 2

Therefore ,
`m_(2)` = 3/4

Recall , for the two lines to be parallel ,
`m_(1)` =
`m_(2)`

but , -3/4
`\\eq` 3/4 , therefore they are not parallel

Also , for the two lines to be perpendicular ,
`m_(1)`x
`m_(2)` = -1

-3/4 x 3/4 = -9 / 16
`\\eq` -1 , therefore , they are not perpendicular.

In conclusion , the two lines are neither parallel nor perpendicular