Question

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

Answer 1

Answer: neither

Step-by-step 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 $\neq$ 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$\neq$ -1 , therefore , they are not perpendicular.

In conclusion , the two lines are neither parallel nor perpendicular