Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 1 Section 3.4 The Slope- Intercept Form of the Equation of a Line Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1

2 2

3 Slope-Intercept Form In the form of the equation of the line where the equation is written as y = mx + b, if x = 0, then y = b. Therefore, b is the y-intercept for the equation of the line. Furthermore, the x coefficient m is the slope of the line. This form of the equation is called the “Slope- Intercept Form” since we can easily see both of these, the slope and the y-intercept, in the actual equation.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 4 Slopes of Lines Slope-Intercept Form of the Equation of a Line y = mx + b with slope m, and y-intercept b Examples

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 5 Find the slope and y-intercept of the line y = 2x – 7 The slope is 2. Slope-Intercept Form

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 6 Slopes of LinesEXAMPLE SOLUTION Give the slope and y-intercept for the line whose equation is: Subtract 3x from both sides Simplify Hint: You should solve for y so as to have the equation in slope intercept form.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 7 EXAMPLE EXAMPLE Find the slope and y-intercept of the line 2x + 3y = 9 Slope – Intercept Form

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 8 8 Objective #1: Examples

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 9 9 Objective #1: Examples

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 10 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 10 Objective #1: Examples

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 11 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 11 Objective #1: Examples

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 12 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 12

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 13 Slopes of Lines Graphing y = mx + b Using the Slope and y-Intercept 1) Plot the point containing the y-intercept on the y-axis. This is the point (0,b). 2) Obtain a second point using the slope, m. Write m as a fraction, and use rise over run, starting at the point on the y-axis, to plot this point. 3) Use a straightedge to draw a line through the two points. Draw arrowheads at the ends of the line to show that the line continues indefinitely in both directions

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 14 Graphing LinesEXAMPLE SOLUTION Graph the line whose equation is y = 2x + 3. The equation y = 2x + 3 is in the form y = mx + b. Now that we have identified the slope and the y-intercept, we use the three steps in the box to graph the equation. The slope is 2 and the y-intercept is 3.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 15 Graphing Lines 1) Plot the point containing the y-intercept on the y-axis. The y-intercept is 3. We plot the point (0,3), shown below. CONTINUED (0,3)

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 16 Graphing Lines 2) Obtain a second point using the slope, m. Write m as a fraction, and use rise over run, starting at the point containing the y-intercept, to plot this point. We express the slope, 2, as a fraction. CONTINUED (0,3) We plot the second point on the line by starting at (0, 4), the first point. Based on the slope, we move 2 units up (the rise) and 1 unit to the right (the run). This puts us at a second point on the line, (1, 5), shown on the graph. (1,5)

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 17 Graphing Lines 3) Use a straightedge to draw a line through the two points. The graph of y = 2x + 3 is show below. CONTINUED (0,3) (1,5)

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 18 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 18 Objective #2: Examples

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 19 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 19 Objective #2: Examples

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 20 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 20 Objective #2: Examples

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 21 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 21 Objective #2: Examples

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 22 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 22

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 23 Graph using the Slope and y-Intercept Earlier in this chapter, we considered linear equations of the form. We used x- and y-intercepts, as well as checkpoints, to graph these equations. It is also possible to obtain graphs by using the slope and y-intercept. To do this, begin by solving for y. This will put the equation in slope-intercept form. Then use the three-step procedure to graph the equation.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 24 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 24 Objective #3: Example

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 25 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 25 Objective #3: Example

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 26 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 26 Objective #3: Example

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 27 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 27

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 28 Slope as Rate of ChangeEXAMPLE A linear function that models data is described. Find the slope of each model. Then describe what this means in terms of the rate of change of the dependent variable y per unit change in the independent variable x. The linear function y = 2x + 24 models the average cost, y in dollars of a retail drug prescription in the United States, x years after SOLUTION The slope of the linear model is 2. This means that every year (since 1991) the average cost in dollars of a retail drug prescription in the U.S. has increased approximately $2.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 29 Linear ModelingEXAMPLE Find a linear function, in slope-intercept form or a constant function that models the given description. Describe what each variable in your model represents. Then use the model to make a prediction of the number of U.S. Internet users in SOLUTION In 1998, there were 84 million Internet users in the United States and this number has increased at a rate of 21 million users per year since then. I(x) = 21x + 84, where I(x) is the number of U.S. Internet users (in millions) x years after We predict in 2010, there will be I(12) = 21(12) + 84 = 336 million U.S. Internet users.

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 30 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 30 Objective #4: Examples

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 31 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 31 Objective #4: Examples

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 32 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 32 Objective #4: Examples

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 33 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 33 Objective #4: Examples

Copyright © 2013, 2009, 2006 Pearson Education, Inc. 34 Copyright © 2013, 2009, 2006 Pearson Education, Inc. 34 Objective #4: Examples