# GED Math : Parallel and Perpendicular Lines

## Example Questions

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### Example Question #807 : Geometry And Graphs

Which of the following lines is parallel to a line having a slope of  ?

Explanation:

Which of the following lines is parallel to a line having a slope of  ?

For lines to be parallel, the slopes must be equal. That is the only way for the two lines to continuously run without ever crossing.

So, we should look for a line with a slope of

At first glance, there are not options. However, begin by eliminating any options which are already solved for y, which do not have the right slope.

So,

and

can be eliminated...

This leaves us with two options. For each option, divide both sides by the coefficient in front of the y, and simplify.

Now, does 55 over 14 equal 5 over 4? No, it is more like 3.9 than 1.25

This leaves us with our final option:

If we simplify we see that this should indeed be parallel.

### Example Question #808 : Geometry And Graphs

If the green line has an equation

And if the blue line is perpendicular to the green line, what is the equation of the blue line?

Explanation:

Recall that perpendicular slopes are opposite and reciprocal.

So to get the slope of the blue line, all we need to do it to switch the sign on the green line and "flip-flop" the value

Green slope:

Blue slope:

Now all we need is the y-intercept, which we can tell by looking at the graph. We can see that when x=0, y=-1. So our y-intercept is =-1.

This gives us our final answer of

### Example Question #809 : Geometry And Graphs

The line  is graphed on a coordinate plane. Which of the following lines will be parallel to it?

Explanation:

When determining if one line is perpendicular or parallel to another, it's important to observe the slopes of the lines. Lines are parallel if they share the same slope. They must have the same "m" value. This can be easily assessed as long as the lines are in  form. Lines will be perpendicular if the product of the two slopes equals . This means that the m values will be the negative inverse of each other when comparing two line equations.

The equation of the graphed line is . Since it is already in  form, we can quickly deduce that the slope is  Therefore, another line that also has a slope of  will be parallel to it. The only option is . The y-intercept value does not matter.

### Example Question #810 : Geometry And Graphs

The line  is graphed on a coordinate plane. Which of the following lines will be perpendicular to it?

Explanation:

When determining if one line is perpendicular or parallel to another, it's important to observe the slopes of the lines. Lines are parallel if they share the same slope. They must have the same "m" value. This can be easily assessed as long as the lines are in  form. Lines will be perpendicular if the product of the two slopes equals . This means that the m values will be the negative inverse of each other when comparing two line equations.

The equation of the graphed line is . Since it is already in  form, we can quickly deduce that the slope is  Therefore, aline that has a slope of  will be perpendicular to it. The only option is . The y-intercept value does not matter.

### Example Question #91 : Coordinate Geometry

The line  is graphed on a coordinate plane. Which of the following lines will be parallel to it?

Explanation:

When determining if one line is perpendicular or parallel to another, it's important to observe the slopes of the lines. Lines are parallel if they share the same slope. They must have the same "m" value. This can be easily assessed as long as the lines are in  form. Lines will be perpendicular if the product of the two slopes equals . This means that the m values will be the negative inverse of each other when comparing two line equations.

For this problem, the first step is to rewrite the graphed equation so it is in  form. Just keep in mind that what you do to one side, you must do to the other.

Now we know that the slope of the graphed equation is . This means that for another line to be parallel, the second line must also have a slope of

The only provided option is . The y-intercept does not matter.

### Example Question #92 : Coordinate Geometry

The line  is graphed on a coordinate plane. Which of the following lines will be perpendicular to it?

Explanation:

When determining if one line is perpendicular or parallel to another, it's important to observe the slopes of the lines. Lines are parallel if they share the same slope. They must have the same "m" value. This can be easily assessed as long as the lines are in  form. Lines will be perpendicular if the product of the two slopes equals . This means that the m values will be the negative inverse of each other when comparing two line equations.

For this problem, the first step is to rewrite the graphed equation so it is in  form. Just keep in mind that what you do to one side, you must do to the other.

Now we know that the slope of the graphed equation is . This means that for another line to be perpendicular, the second line must have a slope of

The only provided option is . The y-intercept does not matter.

### Example Question #41 : Parallel And Perpendicular Lines

Which of the following is parallel to the line ?