Linear Functions Lesson 2: Slope of Parallel and Perpendicular Lines

Today’s Objectives Demonstrate an understanding of slope with respect to: rise and run; rate of change; and line segments and lines. Apply a rule for determining whether two lines are parallel or perpendicular Solve problems involving slope

Vocabulary - Review Slope The measure of a lines steepness (vertical change/horizontal change) Rise The vertical change of a line Run The horizontal change of a line

Parallel Lines Parallel lines are straight lines that do not meet; they remain the same distance apart. In order for two lines to stay parallel, they must have the same rise and the same run over the same space. In other words, they must have the same slope. For example, if the slope of one parallel line is 2/3, the slope of the other parallel line must also be 2/3.

Example Line EF passes through E(-3,-2) and F(-1,6). Line CD passes through C(-1,-3) and D(1,7). Line AB passes through A(-4,2) and B(-5,-2). Which of these lines are parallel? Why? Determine the slope of each line. EF ( / ) = 8/2 = 4 CD ( / ) = 10/2 = 5 AB( / ) = -4/-1 = 4 Lines EF and AB are parallel because they both have a slope of 4.

Perpendicular Lines Perpendicular lines are lines that meet at a 90 degree angle. In order to be perpendicular, the slope of one line must be the negative reciprocal of the slope of the other line. For example, if the slope of one perpendicular line is 2/3, the slope of the other perpendicular line must be: -3/2.

Example The points A(2,-6) and B(4,-3) lie on a line. A) Find the slope of a line parallel to this line m = [-3-(-6)]/4-2 m = 3/2 B) Find the slope of a line perpendicular to this line -2/3 Solution: Use the given points in the slope formula to find the original slope, then, take the negative reciprocal to find the slope of the perpendicular line.

A B C Classifying Shapes The ability to classify lines as either perpendicular or parallel is helpful when classifying shapes such as triangles, parallelograms, and rectangles. Example: Is triangle ABC a right triangle? A(5,8) B(0,5) C(3,0)

A B C Example Side AB 8-5/5-0 = 3/5 Side BC 0-5/3-0 = -5/3 Sides AB and BC are perpendicular So this is a right triangle Solution: Measure the slopes of the three lines connecting the points. If two of the slopes are negative reciprocals of each other then we know this is a right triangle.

Identifying a Line Perpendicular to a Given Line

E G F Solution to B): To find the point G, draw line EF on a graph. The slope of line EG must be -3/2 as it is perpendicular to line EF. From point E, we can count out a rise of -3, and a run of 2 to find a point, G (4, 0). Draw a line through EG on the graph to see that it is perpendicular

J (3,6) H G J (-7,0) Practice: On the following graph, determine the slope of a line that is perpendicular to the line through G(-2,3) and H(1,-2). Determine the coordinates of J so that line GJ is perpendicular to line GH.

HOMEWORK 6.1 – page 339 # 4, 5, 6, 11, 13iii, iv, 16, 17, 21a, 22, 24a, – page 349 # 3ad, 4bd, 8ac, 9ac, 10a, 12, 15, 17