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 [tex]m_{1}[/tex] is the slope of the first line and [tex]m_{2}[/tex] is the slope of the second line , then
[tex]m_{1}[/tex] x [tex]m_{2}[/tex] = -1
[tex]m_{1}[/tex] = -1/ [tex]m_{2}[/tex]
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 [tex]m_{1}[/tex] = -3/4
To find [tex]m_{2}[/tex] , 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 , [tex]m_{2}[/tex] = 3/4
Recall , for the two lines to be parallel , [tex]m_{1}[/tex] = [tex]m_{2}[/tex]
but , -3/4 [tex]\neq[/tex] 3/4 , therefore they are not parallel
Also , for the two lines to be perpendicular , [tex]m_{1}[/tex]x [tex]m_{2}[/tex] = -1
-3/4 x 3/4 = -9 / 16[tex]\neq[/tex] -1 , therefore , they are not perpendicular.
In conclusion , the two lines are neither parallel nor perpendicular
