Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 4.2 - 1.

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Copyright © 2010 Pearson Education, Inc. All rights reserved Sec

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec Graphs, Linear Equations, and Functions Chapter 4

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec Slope of a Line

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Objectives 1.Find the slope of a line, given two points on the line. 2.Find the slope of a line, given an equation of the line. 3.Graph a line, given its slope and a point on the line. 4.Use slopes to determine whether two lines are parallel, perpendicular, or neither. 5.Solve problems involving average rate of change.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Find the Slope of a Line Given Two Points on the Line One of the important properties of a line is the rate at which it is increasing or decreasing. The slope is the ratio of vertical change, or rise, to horizontal change, or run. 12 ft 4 ft P1P1 P2P2 As we move from P 1 to P 2 :

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Find the Slope of a Line Given Two Points on the Line

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Finding the Slope of a Line Find the slope of the line containing the points (–3, 1) and (3, 3). Rise = 3 – 1 = 2 Run = 3 – (–3) = 6 There is a rise of 1 unit for a run of 3 units.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Find the Slope of a Line given Two Points on the Line

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Find the Slope of a Line Given the Equation of the Line

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Finding the Slope of Horizontal and Vertical Lines Find the slope of the line containing the points (–3, 2) and (4, 2). Find the slope of the line containing the points (1, 3) and (1, –2). Since the slope is 0, this is a horizontal line. Since the slope is undefined, this is a vertical line.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Finding the Slope from an Equation

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Using the Slope and a Point to Graph a Line Locate the point P(–5, 5). From the slope formula: So, move down 2 units and then 3 units to the right to the point R(–2, 3). Down 2 Right 3 P R

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Orientation of a Line in the Plane

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Slopes of Parallel and Perpendicular Lines Since parallel lines have the same slope, any line parallel to this line will have slope –2.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Slopes of Parallel and Perpendicular Lines

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Slopes of Parallel and Perpendicular Lines

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Slope of a Line Interpreting Slope as Average Rate of Change Cindy purchased a new care in 2001 for $18,000. In 2006, the car had a value of $7500. At what rate is the car’s value changing with respect to time?