Chapter 3 Graphing Linear Equations Section 5 Parallel

Concept Parallel Lines Two nonvertical lines are parallel if they have the same slope.

Example Parallel Lines Are the two lines parallel? 1 The slope of the first

Example Are the two lines 15 x – 3 y = 12 and y

Concept Perpendicular Lines Two nonvertical lines are perpendicular if their slopes are negative reciprocals.

Example Perpendicular Lines 3 Are the two lines perpendicular ? The slope of the

Example 4 Are the two lines 4 x + 5 y = 10 and

Concept 5 Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 8

Concept 6 Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 9

Concept 7 Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 10

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Concept Parallel Lines Two nonvertical lines are parallel if they have the same slope. In other words, if the slope of one line is and the slope of the other line is the two lines are parallel if If two lines are both vertical lines, they are parallel. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 2

Example Parallel Lines Are the two lines parallel? 1 The slope of the first line is − 4. The slope of the second line is also − 4. The lines are parallel. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 3

Example Are the two lines 15 x – 3 y = 12 and y = 5 x + 3 parallel? 2 To find the slope of the first line, we solve the equation for y: Subtract 15 x from both sides. Divide by – 3. The slope of the first line is 5. Since the second line is already in slope-intercept form, we see that the slope of that line is also 5. Since the two slopes are equal, the two lines are parallel. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 4

Concept Perpendicular Lines Two nonvertical lines are perpendicular if their slopes are negative reciprocals. In other words, if the slope of one line is and the slope of the other line is the two lines are perpendicular if A vertical line is perpendicular to a horizontal line. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 5

Example Perpendicular Lines 3 Are the two lines perpendicular ? The slope of the first line is The slope of the second line is The lines are perpendicular. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 6

Example 4 Are the two lines 4 x + 5 y = 10 and parallel, perpendicular, or neither? Solve the equation for y: The slope of this line is 4/5. Since the slopes are equal, the lines are parallel. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 7