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Slopes of Parallel and Perpendicular Lines

HSG-GPE.B.5
Answer Keys Here

Aligned To Common Core Standard:

Expressing Properties - HSG-GPE.B.5

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=(y2 - y1)/(x2 - x1) 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. These worksheets and lessons show students how to use what we know about the slope of parallel or perpendicular lines to your advantage.

Printable Worksheets And Lessons




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?