ACT Math : How to find out if lines are parallel

Study concepts, example questions & explanations for ACT Math

varsity tutors app store varsity tutors android store varsity tutors amazon store varsity tutors ibooks store

Example Questions

Example Question #21 : Coordinate Geometry

Which of the following lines is parallel to:

 

Possible Answers:

Correct answer:

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 #4 : How To Find Out If Lines Are Parallel

Which pair of linear equations represent parallel lines?

Possible Answers:

y=x+2

y=-x+2

y=2x+4

y=x+4

y=x-5

y=3x+5

y=-x+4

y=x+6

y=2x-4

y=2x+5

Correct answer:

y=2x-4

y=2x+5

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 "m" spot in the linear equation (y=mx+b)

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

Example Question #5 : How To Find Out If Lines Are Parallel

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

Possible Answers:

Correct answer:

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 #41 : Coordinate Plane

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?

Possible Answers:

Yes, the lines are parallel with a slope of .

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 .

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

Correct answer:

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 #42 : Coordinate Plane

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?

Possible Answers:

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

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

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

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

Correct answer:

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.

Learning Tools by Varsity Tutors