Section 3 3 The Slope of a Line

Section 3. 3 The Slope of a Line Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.

Slope In a coordinate plane, the slope of a straight line is defined by the change in y divided by the change in x. y 4 3 2 Change in y = 2 1 4 3 2 1 2 3 4 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. (0, 2) (3, 0) 1 2 3 Change in x=3 2 4 x

Definition of Slope of a Line The slope of any nonvertical line that contains the points with coordinates (x 1, y 1) and (x 2, y 2) is defined by the difference ratio where x 2 x 1. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 3

Example Find the slope of the line that passes through (3, 6) and (1, 2). Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 4

Example Find the slope of the line that passes through ( 3, 2) and (2, 4). Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 5

Example Find the slope of the line that passes through (0, 2) and (5, 2). Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 6

Example Find the slope of the line that passes through ( 4, 0) and ( 4, 4). Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 7

Types of Slope Positive Slope Line goes up to the right y 1. Lines with positive slopes go upward as x increases. x y Negative Slope Line goes downward to the right x 2. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Lines with negative slopes go downward as x increases. 8

Types of Slope Zero Slope y 3. Horizontal Line Horizontal lines have a slope of 0. x Undefined Slope y 4. Vertical Line A vertical line has an undefined slope. x Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 9

Slope-Intercept The slope-intercept form of the equation of a line that has slope m and y-intercept (0, b) is given by y = mx + b. y = 3 x – 4 y The slope The -intercept is is 3. (0, -4). The slope y-intercept is is Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 10

Example What is the slope and the y-intercept of the line 5 x + 3 y = 2? Solve the equation for y. The slope is -5/3. The y -intercept is (0, 2/3). Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 11

Example Find the equation of the line with slope (0, 5). Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. and y-intercept 12

Example Graph the line with slope and y-intercept (0, 2). y 4 3 (0, 2) 2 3 units down 2 units to the right rise 1 x 4 3 2 1 2 1 run 2 3 (2, 1) 3 4 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 4 13