### All ACT Math Resources

## Example Questions

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

Which of the following lines is parallel to:

**Possible Answers:**

**Correct answer:**

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 #1 : How To Find Out If Lines Are Parallel

Which pair of linear equations represent parallel lines?

**Possible Answers:**

**Correct answer:**

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 #3 : 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:**

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 #4 : 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?

**Possible Answers:**

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

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 .

**Correct answer:**

Yes, the lines are parallel with a slope of .

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 #5 : 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?

**Possible Answers:**

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 .

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

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.

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