Chapter 3 Section 4 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Equations of a Line Write an equation of a line by using its slope and y -intercept. Graph a line by using its slope and a point on the line. Write an equation of a line by using its slope and any point on the line. Write an equation of a line by using two points on the line. Find an equation of a line that fits a data set. 5 5

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1 Objective 1 Slide Write an equation of a line by using its slope and y-intercept.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Find an equation of the line with slope −1 and y-intercept (0,8). EXAMPLE 1 Finding an Equation of a Line Solution: Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Objective 2 Graph a line by using its slope and a point on the line. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Graph a line by using its slope and a point on the line. Slide Step 1: Write the equation in slope-intercept form, if necessary, by solving for y. Step 2: Identify the y-intercept. Graph the point (0,b). Step 3: Identify slope m of the line. Use the geometric interpretation of slope (“rise over run”) to find another point on the graph by counting from the y-intercept. Step 4: Join the two points with a line to obtain the graph.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 2 Solution: Graphing a Line by Using the Slope and y-intercept Slide Graph 3x – 4y = 8 by using the slope and y-intercept. Slope intercept form

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 3 Solution: Graphing a Line by Using the Slope and a Point Slide Graph the line through (2,−3) with slope. Make sure when you begin counting for a second point you begin at the given point, not at the origin.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3 Objective 3 Write an equation of a line by using its slope and any point on the line. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Write an equation of a line by using its slope and any point on the line. There is another form that can be used to write the equation of a line. To develop this form, let m represent the slope of a line and let (x 1,y 1 ) represent a given point on the line. Let (x, y) represent any other point on the line. The point-slope form of the equation of a line with slope m passing through point (x 1,y 1 ) is This result is the point-slope form of the equation of a line. Slide Slope Given point

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 4 Solution: Using the Slope-Intercept Form to Write an Equation Slide Write an equation, in slope-intercept form, of the line having slope −2 and passing through the point (−1,4). The slope-intercept form is

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 5 Solution: Using the Point-Slope Form to Write Equations Slide Find the equation of the line through (5,2), with the slope Give the final answer in slope-intercept form.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4 Objective 4 Write an equation of a line by using two points on the line. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 6 Solution: Finding the Equation of a Line by Using Two Points Slide Find an equation of the line through the points (2,5) and (−1,6). Give the final answer in slope-intercept form. The same result would also be found by substituting the slope and either given point in slope-intercept form and then solving for b.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Standard Form Slide Many of the linear equations in Section 3.1−3.3 were given in the form Ax + By = C, called standard form, which we define as follows. A linear equation is in standard form if it is written as where A, B, and C are integers, A > 0, and B ≠ 0.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley A summary of the forms of linear equations follow Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5 Objective 5 Find an equation of a line that fits a data set. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 7 Solution: Finding the Equation of a Line That Describes Data Slide Use the points (1, 3362) and (7, 5491) to find an equation in slope-intercept form that approximates the data of the table. (Round the slope to the nearest tenth.) How well does this equation approximate the cost in 2003? The equation gives y ≈ 4781 when x = 5, which is a pretty good approximation.