# PSAT Math : How to find the slope of parallel lines

## Example Questions

### Example Question #13 : Coordinate Geometry

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

y = 4x + 7

y = –4x + 7

y = (1/4)x + 7

y = 4x – 7

y = 4x + 7

Explanation:

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

### Example Question #14 : Coordinate Geometry

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?

–7

13

–13

1

7

–7

Explanation:

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 #11 : Coordinate Geometry

Line  is represented by the equation .

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

Explanation:

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

3a = 14

a = 14/3

### Example Question #101 : Psat Mathematics

Which of the following lines is parallel to ?

Explanation:

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 #1 : How To Find The Slope Of Parallel Lines

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