Determine if the following pairs of lines are parallel, perpendicular, or neither: Line 1: y = 4/5x - 5
Line 2: 5x+4y = 6

Line 1 passes through (5, -9) and (0, -5)

We are going to use slope-intercept form of a linear equation.

First we are going to find the slope of the line.

m= -5- (-9)

      0-5

m=4/-5

Now substitute in the point to find the y-intercept:

Either point can be used.  I am using point (0,-5)

y=-4/5x+b

-5=-4/5(0)+b

-5=b

So, the linear equation is  y=-4/5x-5

Line 2 passes through (-3, 8) and (1, 3)

m=3-8

    1-(-3)

m=-5/4

Use slope intercept form and substitute in either point

I am using point (1,3)

y=-5/4x+b

3=-5/4(1)+b

3=-5/4+b

3+5/4=b

17/4=b

Therefore, the equation of Line 2 is y= -5/4x+17/4

Line 1:  y=-4/5x-5           Line 2:  y=-5/4x+17/4

Are the lines parallel?  NO  For lines to be parallel the slopes of both lines must be the same

Are the lines perpendicular?  NO   For lines to be perpendicular the slopes of the lines must be negative reciprocals.

ANSWER:  Neither

Hope this helps!!!