# ACT Math : How to find out if lines are parallel

## Example Questions

### Example Question #26 : Parallel Lines

Which of the following lines is parallel to:

Explanation:

First write the equation in slope intercept form. Add  to both sides to get . Now divide both sides by  to get . The slope of this line is , so any line that also has a slope of  would be parallel to it. The correct answer is  .

### Example Question #27 : Parallel Lines

Which pair of linear equations represent parallel lines?

Explanation:

Parallel lines will always have equal slopes. The slope can be found quickly by observing the equation in slope-intercept form and seeing which number falls in the "" spot in the linear equation

We are looking for an answer choice in which both equations have the same value. Both lines in the correct answer have a slope of 2, therefore they are parallel.

### Example Question #28 : Parallel Lines

Which of the following equations represents a line that is parallel to the line represented by the equation ?

Explanation:

Lines are parallel when their slopes are the same.

First, we need to place the given equation in the slope-intercept form.

Because the given line has the slope of , the line parallel to it must also have the same slope.

### Example Question #1 : How To Find Out If Lines Are Parallel

Line  passes through the points  and . Line  passes through the point  and has a  of . Are the two lines parallel? If so, what is their slope? If not, what are their slopes?

Yes, the lines are parallel with a slope of .

No, the lines are not parallel. Line  has a slope of  and line  has slope .

No, the lines are not parallel. Line  has a slope of  and line  has a slope of .

Yes, the lines are parallel with a slope of .

Yes, the lines are parallel with a slope of .

Explanation:

Finding slope for these two lines is as easy as applying the slope formula to the points each line contains. We know that line  contains points  and , so we can apply our slope formula directly (pay attention to negative signs!)

.

Line  contains point  and, since the y-intercept is always on the vertical axis, . Thus:

The two lines have the same slope, , and are thus identical.

### Example Question #2 : How To Find Out If Lines Are Parallel

Line  is described by the equation . Line  passes through the points  and . Are the two lines parallel? If so, what is their slope? If not, what are their slopes?

No, the lines are not parallel. Line  has slope  and line  has slope .

Yes, the lines are parallel, and both lines have slope .

Yes, the lines are parallel, and both lines have slope .

No, the lines are not parallel. Line  has slope  and line  has slope .

No, the lines are not parallel. Line  has slope  and line  has slope .

Explanation:

We are told at the beginning of this problem that line  is described by  . Since  is our slope-intecept form, we can see that  for this line. Since parallel lines have equal slopes, we must determine if line  has a slope of .

Since we know that  passes through points  and , we can apply our slope formula:

Thus, the slope of line  is 1. As the two lines do not have equal slopes, the lines are not parallel.