# GED Math : Parallel and Perpendicular Lines

## Example Questions

### Example Question #797 : Geometry And Graphs

Identify the slope of the line perpendicular to the given linear equation.

Explanation:

Identify the slope of the line perpendicular to the given linear equation.

Perpendicular lines intersect at 90 degree angles. To find the slope of a line perpendicular to another known line, we need to take find the opposite reciprocal of our known slope.

The reciprocal of a fraction is simply what we get when we flip a fraction.

Thus, we get:

All we did was exchange our numerator.

However, we also need "the opposite" this means that we also change the sign of our slope.

So, our new slope is

### Example Question #798 : Geometry And Graphs

Which of the following lines is parallel to the line with the equation ?

Explanation:

Start by putting the given line in slope-intercept form.

Recall that parallel lines have the same slope.

Thus,  must be parallel to the given line.

### Example Question #799 : Geometry And Graphs

Which of the following lines is perpendicular to the line with the equation ?

Explanation:

Start by putting the given equation of a line into slope-intercept form.

Recall that perpendicular lines have slopes that are negative reciprocals of each other. Thus,  is the only line that has a slope that is the negative reciprocal of .

### Example Question #800 : Geometry And Graphs

Which of the following lines is perpendicular to the following function?

Explanation:

Which of the following lines is perpendicular to the following function?

Perpendicular lines have opposite reciprocal slopes.

What is the slope of our given equation? To find this, we need to move the negative four over to the right hand side of the equation.

So, our original slope is -1

The opposite reciprocal of -1 is 1

So our answer must have a slope of 1

### Example Question #801 : Geometry And Graphs

Which of the following lines is perpendicular to the line with the equation ?

Explanation:

Start by re-arranging the given equation into slope-intercept form.

Recall that perpendicular lines have slopes that are negative reciprocals of each other. This means that the line that is perpendicular to the given one has a slope of .

is the only line with that slope.

### Example Question #81 : Coordinate Geometry

A line on the coordinate plane has slope . Give the slope of a line perpendicular to this line.

Explanation:

If the slope of a line is given, the slope of a line perpendicular to it is the additive inverse of the reciprocal of the slope of the first line. Thus, the slope sought is

.

### Example Question #803 : Geometry And Graphs

Which of the following lines is perpendicular to the line with the equation ?

Explanation:

Start by converting the standard form of the linear equation to the slope-intercept form.

Recall that lines that are perpendicular must have slopes that are negative reciprocals.

Thus the slope of a line that is perpendicular to the given one must be . The line with the equation  is the only one that has the correct slope.

### Example Question #804 : Geometry And Graphs

Which of the following lines is perpendicular to the line with the equation ?

Explanation:

Recall that perpendicular lines have slopes that are negative reciprocals of each other. Thus, rewrite the given equation in slope-intercept form to find its slope.

Since the given equation has a slope of , the line perpendicular to it must have a slope of  is the only line with the correct slope.

### Example Question #805 : Geometry And Graphs

Which of the following lines is parallel to the line with the equation ?

Explanation:

Recall that parallel lines must have the same slope. Start by putting the given equation into slope-intercept form.

Since the given equation has a slope of , the only line with the same slope is .

### Example Question #806 : Geometry And Graphs

Which of the following lines is perpendicular to the line below?

Explanation:

Which of the following lines is perpendicular to the line below?

Perpendicular lines have slopes which are the opposite signed reciprocal of eachother.

What this means is that to find perpendicular slopes, we need to change the sign of our original slope, and then flip the numerator and the denominator.

You might be thinking, but what is the numerator and what is the denominator of a whole number?

Well, we can picture any whole number as having a denominator of 1. This means that we can get our reciprocal via the following.

We're almost there, by we also need to change the sign:

So, our answer must have a slope of one-fourteenth.