# Algebra

Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = –3/4x+2

3x-4y=-8

A.parallel
C.neither

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1. Hey, A Child!

Once again, you are dealing with systems of equations. Except this time, it is graphing them.
Before I start....I want to define the terms real quick.
Parallel means they run side-by-side in a straight line slanting upwards, but never intersect. If an equation is parallel it normally does not give an ordered coordinate pair.
Perpendicular means they intersect at one point and then continue in the direction infinitely.

To graph them, solve for X and Y first.
The best way to do this is to use substitution (at least for this equation)

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

Step 1:Solve y = -3/4x + 2 for y
Notice that the value of y is already given; -3/4x + 2

So, substitute -3/4x + 2 for y in 3x - 4y = -8
3x - 4y = -8
3x - 4(-3/4x + 2) =-8
6x - 8 = -8
6x - 8 + 8 = -8+ 8
6x = 0
x = 0

Step 2: Substitute 0 for in y = -3/4x + 2

y = -3/4x + 2
y = -3/4(0) + 2
y = 2

So, x = 0 and y = 2. This is where the points will intersect.
Since it is where the points intersect, it is perpendicular.
You can also graph it to determine if it is parallel or perpendicular by calculating the slope and Y intercept.

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2. y = –3/4x+2
slope = -3/4

3x-4y=-8
slope = 3/4

Just because two lines intersect does not mean they are perpendicular.
Also, perpendicular means that the two slopes multiply to a product of -1.

Neither parallel nor perpendicular

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