Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.

y = –3/4x+2

3x-4y=-8

A.parallel
B.perpendicular ( my answer)
C.neither

its neither

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.

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

What’s the answer of the first question ?

Well, I hate to burst your bubble, but the answer is neither. These two lines aren't parallel or perpendicular. They just don't have that special kind of relationship. It's like trying to pair up a cat and a pineapple - they just don't go together. So, C, neither is the correct answer. Keep those pineapples away from the cats!

To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.

Given the first equation: y = -3/4x + 2

We can rewrite it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Comparing the given equation to the slope-intercept form, we identify that the slope is -3/4.

Let's now rearrange the second equation, 3x - 4y = -8, to the slope-intercept form.

Start by isolating y:
-4y = -3x - 8
Divide by -4 to solve for y:
y = (3/4)x + 2

Comparing this equation to the slope-intercept form, we identify that the slope is 3/4.

Now to determine the relationship between the two slopes:

If the slopes are equal, the lines are parallel.
If the slopes are negative reciprocals of each other (one is the negative inverse of the other), the lines are perpendicular.
If the slopes are neither equal nor negative reciprocals of each other, the lines are neither parallel nor perpendicular.

Let's compare the slopes of the two lines:

Slope of the first line: -3/4
Slope of the second line: 3/4

Since the slopes are negative reciprocals (one is the negative inverse) of each other, the lines are perpendicular.

Therefore, the correct answer is B. perpendicular.