# Slopes of Parallel and Perpendicular Lines Worksheets

A pair lines that never intersect are called parallel. Because they never come in contact with one another they must be pitched at the same exact level and as a result two lines that are parallel must have the same slope. In the equation of a line y = mx + b. The variable m stands for the slope. A pair of lines that meet each other at a right angle (90 degrees) are said to be perpendicular. As a result, their slopes are negative reciprocals of one another. That means that what ever the fraction of one line slope is, the other is the reciprocal of that fraction taken with a negative symbol thrown at it. For example, if a line had a slope of 5/6, a line perpendicular to it would have the slope of -6/5 or -1 1/5. These worksheets and lessons show students how to use what we know about the slope of parallel or perpendicular lines to your advantage.

### Aligned Standard: High School Geometry - HSG-GPE.B.5

- Analyze Slope Step-by-step Lesson - Based on the slope, are the lines parallel or perpendicular?
- Guided Lesson - This is a neat skill to practice. Sometimes I sketch the line to determine it.
- Guided Lesson Explanation - I revert back to the concepts laid out by the slop-intercept form to work on this.
- Practice Worksheet - Man, there are a whole lot of line Cs and D!
- Matching Worksheet - You to pay attention in this one and you will be rewarded.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

When you have the same slope as another line, that says a lot about you.

- Homework 1 - Two parallel lines have the same slope.
- Homework 2 - The slope-intercept form of a liner equation is Y = mx + b.
- Homework 3 - Use the slope of line k and a point on line k to find its y-intercept.

### Practice Worksheets

We use to have a running joke in one of my math classes. It went something like this, "Have a different slope than others?"

- Practice 1 - Perpendicular lines have slope that are opposite reciprocals, like (a/b) and (-b/a) the slope also have a product of -1.
- Practice 2 - Line k, which is perpendicular to line j, includes the point (-14, 10). What is the equation of line k?
- Practice 3 - Line c has a slope of (-25/4). Lined has a slope of (-25/4) are line c and d parallel or perpendicular?

### Math Skill Quizzes

They are all about determine if a line set is parallel or perpendicular.

- Quiz 1 - Use the slope of line k and the y-intercept of line k to find the equation of the line.
- Quiz 2 - Line k is perpendicular to j, so its slope is the opposite reciprocal.
- Quiz 3 - What is the equation of line k?

### How to Find the Slope of Parallel and Perpendicular Lines

Finding equations of straight lines and curves is an important concept in coordinate geometry. The first step when finding the equation of a straight line is to find the slope of the line. The slope of the line is "rise over run" and measures the steepness of a straight line.

The formula to calculate the slope of a straight line is; m = (y_{2} - y_{1})/(x_{2} - x_{1})

An equation of a straight line is given by; y = mx + c. Where "m" is the slope of the line.

Did you know that you can find out the slope of the line from a line perpendicular or parallel to it? Well, yes, that is very much possible.

**Case 1: Parallel Lines** - When you are dealing with parallel lines, the slope is equal. Any two equations that have the same value of "m" is an indication that two lines are parallel.

**Case 2: Perpendicular Lines** - When dealing with perpendicular lines, the slope of two lines is negative reciprocals of each other. If a line has a slope of 2, a line perpendicular to it will have a slope of -1/2. The product of the slope of two perpendicular lines is equal to -1.

### Where Are These Found in The Real World?

Parallel lines are found in just about all forms of structural or mechanical structures because they provide a sound and solid consistent structure to maintain stability. They are the fundamental base for all trains across the world. If you go to your nearest community that has sidewalks you realize that this structure works well for concrete and cement structures as well. You will find most electrical power lines follow this structure, unless a storm hits. If you go to your nearest high school track you will notice that the lines are entirely placed in this way. If you have a football field within that track and it is numbered, all of those lines and numbers are positioned in this fashion to make official measurements.

A crossroad is the perfect example of an everyday perpendicular line set. Graphing paper and plaid fashion patterns are also based on this pattern. Have you ever played the game Battleship, those coordinates that you are calling out are just the intersection of two lines that would be described as perpendicular as well. The hands on as analog clock are perpendicular at the hours of 3:00 and 9:00 o'clock.