### All PSAT Math Resources

## Example Questions

### Example Question #5 : Parallel Lines

Consider line c to be y= -4x - 7. Which is the reflection of line c across the x-axis?

**Possible Answers:**

y = 4x – 7

y = –4x + 7

y = 4x + 7

y = (1/4)x + 7

**Correct answer:**

y = 4x + 7

A line reflected across the x-axis will have the negative value of the slope and intercept. This leaves y= 4x + 7.

### Example Question #1 : How To Find The Slope Of Parallel Lines

If line J passes through the points (1, 3) and (2, 4) and line K passes through (0, x) and (10, 3), what would be the value of x in order for lines J and K to be parallel?

**Possible Answers:**

1

7

13

–7

–13

**Correct answer:**

–7

Find the slope of line J, (4 – 3)/(2 – 1) = 1

Now use this slope in for the equation of line K of the form y = mx + b for the other point (10, 3)

3 = 10 + b → b = –7

So for the point (0, X) → X = 0 – 7,

so x = –7 when these two lines are parallel.

### Example Question #7 : Parallel Lines

Line is represented by the equation .

If line passes through the points and , and if is parallel to , then what is the value of ?

**Possible Answers:**

**Correct answer:**

We are told that lines *l* and *m* are parallel. This means that the slope of line *m* must be the same as the slope of *l*. Line *l* is written in the standard form of Ax + By = C, so its slope is equal to –A/B, or –2/–3, which equals 2/3. Therefore, the slope of line *m* must also be 2/3.

We are told that line *m* passes through the points (1, 4) and (2, a). The slope between these two points must equal 2/3. We can use the formula for the slope between two points and then set this equal to 2/3.

slope = (a – 4)/(2 – 1) = a – 4 = 2/3

a – 4 = 2/3

Multiply both sides by 3:

3(a – 4) = 2

3a – 12 = 2

Add 12 to both sides:

3a = 14

a = 14/3

### Example Question #11 : Parallel Lines

Which of the following lines is parallel to ?

**Possible Answers:**

**Correct answer:**

Two lines are parallel if they have the same slope. In the equation, represents the line's slope. The correct answer must therefore have a slope of 2. That line is

.

### Example Question #12 : Parallel Lines

In the xy-plane, what is the equation for a line that is parallel to and passes through the point ?

**Possible Answers:**

**Correct answer:**

In order to solve the equation for this line, you need to things: the slope, and at least one point. You are already given a point for the line, so you just need to figure out the slope. The other piece of information you have is a line parallel to the line that you're looking for; since parallel lines have the same slope, you just need to figure out the slope of the parallel line you've already been given.

To figure out the slope, change the equation into point-slope form (*y = *m*x+*b) so the slope *m* is easy to find. To do that, you need to isolate *y* on one side of the equation.

By the calculations above, you'll find that the slope of the parallel line is -1/2.

Now, use this slope of -1/2 and the point 4,1 to find the equation. First, plug them both into the point-slope form, then solve for the slope-intercept form.