Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 3 Introduction to Graphing

3-2 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Slope-Intercept Form Using the y-intercept and the Slope to Graph a Line Equations in Slope-Intercept Form Graphing and Slope-Intercept Form Parallel and Perpendicular Lines 3.6

3-3 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Draw a line that has slope 2/3 and y-intercept (0,  1). Solution We plot (0,  1) and from there move up 2 units and to the right three units. This locates the point (3, 1). We plot the point and draw a line passing through the two points. up 2 y-intercept right 3 (0,  1) (3, 1)

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. The Slope-Intercept Equation The equation y = mx + b is called the slope-intercept equation. The equation represents a line of slope m with y-intercept (0, b).

3-5 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Find the slope and the y-intercept of each line whose equation is given. a)b) 3x + y = 7 c) 4x  5y = 10 Solution a) The slope is. The y-intercept is (0,  2).

3-6 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example b) We first solve for y to find an equivalent form of y = mx + b. 3x + y = 7 y =  3x + 7 The slope is  3. The y-intercept is (0, 7).

3-7 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example c) We rewrite the equation in the form y = mx + b. 4x  5y = 10 The slope is 4/5. The y-intercept is (0,  2).

3-8 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example A line has slope  3/7 and y-intercept (0, 8). Find an equation of the line. Solution We use the slope-intercept equation, substituting  3/7 for m and 8 for b: The desired equation is

3-9 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example up 4 units right 3 down 4 left 3 (  3,  6) (3, 2) (0,  2) Graph: Solution The slope is 4/3 and the y-intercept is (0,  2). We plot (0,  2), then move up 4 units and to the right 3 units. We could also move down 4 units and to the left 3 units. Then draw the line.

3-10 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Graph: 3x + 4y = 12 Solution Rewrite the equation in slope-intercept form.

3-11 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example up 3 down 3 left 4 right 4 (0, 3) (4, 0) (  4, 6) Solution The slope is  3/4 and the y-intercept is (0, 3). We plot (0, 3), then move down 3 units and to the right 4 units. An alternate approach would be to move up 3 units and to the left 4 units.

3-12 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Two lines are perpendicular if they intersect at a right angle. If one line is vertical and another is horizontal, they are perpendicular. Two lines are parallel if they lie in the same plane and do not intersect no matter how far they are extended. Parallel and Perpendicular Lines

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Slope and Parallel Lines Two lines are parallel if they have the same slope or if both lines are vertical.

3-14 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Determine whether the graphs of and 3x  2y =  5 are parallel. Solution Remember that parallel lines extend indefinitely without intersecting. Thus, two lines with the same slope but different y-intercepts are parallel.

3-15 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example The line has slope 3/2 and y-intercept 3. We need to rewrite 3x  2y =  5 in slope-intercept form: 3x  2y =  5  2y =  3x  5 The slope is 3/2 and the y-intercept is 5/2. Both lines have slope 3/2 and different y-intercepts, the graphs are parallel.

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Slope and Perpendicular Lines Two lines are perpendicular if the product of their slopes is –1 or if one line is vertical and the other is horizontal. Thus, if one line has slope m the slope of a line perpendicular to it is –1/m.

3-17 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Determine whether the graphs of 2x + y = 10 and are perpendicular. Solution Write the first equation in slope-intercept form. The slope of the second line is 1/2. The lines are perpendicular the product of their slopes is –1.