2. CHAPTER 3 Graphs of Liner Equations Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 3.1Graphs and Applications of Linear Equations 3.2More with Graphing and Intercepts 3.3Slope and Applications 3.4Equations of Lines 3.5Graphing Using the Slope and the y-Intercept 3.6Parallel and Perpendicular Lines 3.7Graphing Inequalities in Two Variables

3. OBJECTIVES 3.4 Equations of Lines Slide 3Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. aGiven an equation in the form y = mx + b find the slope and the y-intercept; find an equation of a line when the slope and the y-intercept are given. bFind an equation of a line when the slope and a point on the line are given. cFind an equation of a line when two points on the line are given.

4. The equation y= mx + b is called the slope-intercept equation. The slope is m and the y-intercept is (0, b). 3.4 Equations of Lines The Slope-Intercept Equation: y = mx + b Slide 4Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

5. EXAMPLE Solution We first solve for y: 3x – 4y = 9 –4y = –3x + 9 –4 –4 Subtracting 3x Dividing by –4 3.4 Equations of Lines a Given an equation in the form y = mx + b find the slope and the y-intercept AFind the slope and the y-intercept of 3x – 4y = 9. (continued) Slide 5Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

6. EXAMPLE Solution The slope is The y-intercept is 3.4 Equations of Lines a Given an equation in the form y = mx + b find the slope and the y-intercept AFind the slope and the y-intercept of 3x – 4y = 9. Slide 6Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

7. EXAMPLE Solution: We use the slope- intercept equation. Substitute –3.2 for m and 5 for b: y = mx + b y = –3.2x + 5. Substituting 3.4 Equations of Lines a Find an equation of a line when the slope and the y-intercept are given. BA line has slope –3.2 and y-intercept (0, 5). Find an equation of the line. Slide 7Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

8. EXAMPLE Solution: We use the slope-intercept equation. Substitute 0 for m and 4 for b: y = mx + b y = 0x + 4. Substituting y = 4 3.4 Equations of Lines a Find an equation of a line when the slope and the y-intercept are given. CA line has slope 0 and y-intercept (0, 4). Find an equation of the line. Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

9. EXAMPLE Solution: We use the slope-intercept equation. Substitute for m and 0 for b: y = mx + b y = x + 0. Substituting 3.4 Equations of Lines a Find an equation of a line when the slope and the y-intercept are given. DA line has slope and y-intercept (0, 0). Find an equation of the line. Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

10. EXAMPLE Solution: The slope is 3, so the equation is y = 3x + b. The equation is true for (2, 7). Using the point (2, 7), substitute 2 for x and 7 for y and solve for b. y = 3x + b Substituting 3 for m. 7 = 3(2) + b Substituting 2 for x and 7 for y 7 = 6 + b 1 = b Solving for b The equation is y = 3x + 1. 3.4 Equations of Lines b Find an equation of a line when the slope and a point on the line are given. EFind an equation of the line with slope 3 that contains the point (2, 7). Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

11. EXAMPLE Solution: First, find the slope: 3.4 Equations of Lines c Find an equation of a line when two points on the line are given. FFind an equation of the line containing the points (2, 2) and (–6, –4). (continued) Slide 11Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

12. EXAMPLE Solution: Use either point to find b. Substituting 2 for x and 2 for y Solving for b 3.4 Equations of Lines c Find an equation of a line when two points on the line are given. FFind an equation of the line containing the points (2, 2) and (–6, –4). (continued) Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

13. EXAMPLE The equation of the line. 3.4 Equations of Lines c Find an equation of a line when two points on the line are given. FFind an equation of the line containing the points (2, 2) and (–6, –4). Slide 13Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.