Chapter 7 Graphing Equations of Lines and Linear Models; Rates of Change Section 3 Using Slope to Graph Equations of Lines and Linear Models
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1 Math 167 Pre-Statistics Chapter 7 Graphing Equations of Lines and Linear Models; Rates of Change Section 3 Using Slope to Graph Equations of Lines and Linear Models Objectives 1. Use the slope and the y-intercept of a line to sketch the line. 2. Describe the meaning of m for an equation of the form y = mx + b. 3. Graph an equation of the form y = mx + b by using the line s slope and y-intercept. 4. Find an equation of a line from its graph. 5. Graph an equation of a linear model by using the model s slope and vertical intercept. 6. Use a linear model s slope and vertical intercept to find its equation. Vocabulary 1. slope-intercept form 1
2 OBJECTIVE 1 Use the slope and the y-intercept of a line to sketch the line. Sketch the line that has the given slope and y-intercept. 1. m = ' (, (0, 3) 2. m = 0 ', (0, 4) 3. m = 2, (0, 1) 2
3 OBJECTIVE 2 Describe the meaning of m for an equation of the form y = mx + b. 4. a. Use the method discussed in Section 7.1 to graph y = 2x + 1. x y = 2x + 1 (x, y) b. What is the slope of the line y = 2x + 1? c. Compare the slope with the number multiplied times x in the equation y = 2x
4 Finding the Slope and y-intercept from a Linear Equation For a linear equation of the form y = mx + b, the slope of the line is m the y-intercept of the line is (0, b) We say this equation is in slope-intercept form. The graph of the equation y = 3x + 8 is a line with slope 3 and y-intercept (0, 8). Graphing an Equation in Slope-Intercept Form To graph an equation of the form y = mx + b, 1. Plot the y-intercept (0, b). 2. Use m = 9:;< to plot a second point. (Repeat for a third point.) 9=> 3. Sketch the line that passes through the three plotted points. 4
5 OBJECTIVE 3 Graph an equation of the form y = mx + b by using the line s slope and y-intercept. Sketch the graph of each equation by hand using the line s slope and y-intercept. 5. y = 0 x 1 6. y =? x y = 2x 3 ( 0 5
6 OBJECTIVE 4 Find an equation of a line from its graph. 8. Find an equation of a line that has slope ( and y-intercept (0, 2). A Finding an Equation of a Line from a Graph To find an equation of a line from a graph. 1. Determine the slope m and the y-intercept (0, b) from the graph. 2. Substitute your values for m and b into the equation y = mx + b. 9. Find an equation of the line shown in the graph. 6
7 OBJECTIVE 5 Graph an equation of a linear model by using the model s slope and vertical intercept. 10. Let p be the percentage of Americans who watch a greater number of TV programs on channels websites (rather than on TV) at t years since 2005 (see the following table). A reasonable model of the situation is p = 3.7t 0.8. a. Graph the model by hand. Amount of Money (in billions of dollars) Year b. Predict in which year 36% of Americans will watch a greater number of TV programs on channels websites. c. Did you perform interpolation or extrapolation? Do you have much faith in the prediction? Explain. 7
8 OBJECTIVE 6 Use a linear model s slope and vertical intercept to find its equation. 11. A person earns a starting salary of $30 thousand at a company. Each year, the person receives a $2 thousand raise. Let s be the person s salary (in thousands of dollars) after they have worked at the company for t years. a. Is there an exact linear association between t and s? Explain. b. Find the s-intercept of a linear model. What does it mean in this situation? c. Find the slope of the linear model. What does it mean in this situation? d. Find an equation of a linear model. 8
9 12. Let T be the total one-semester cost (in dollars) of tuition plus parking fee for u units (credits or hours) of classes at your college. a. Is there an exact linear association between u and T? If so, find the slope. b. Find an equation of the model. c. Graph the model. 9
10 13. Let s be U.S. retail sales (in billions of dollars) of vitamins and dietary supplements at t years since A reasonable model is s = 1.23t a. Use technology to draw a scatterplot and the model in the same viewing window. Check whether the line comes close to the data points. b. What is the slope of the model? What does it mean in this situation? Year U.S. Retail Sales of Vitamins and Dietary Supplements (billions of dollars)
11 c. Find the rates of change in the number of retails sales from one year in the table to the next one listed. Compare the rates of change with the result you found in Part (b). Year U.S. Retail Sales of Vitamins and Dietary Supplements (billions of dollars) d. What is the s-intercept? What does it mean in this situation? e. Use the model to estimate the retail sales in Did you perform interpolation or extrapolation? Compute the error. 11
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Math 101 Chapter 6 Review Multiple Choice Identif the choice that best completes the statement or answers the question. 1. Determine the slope of this line segment. A x 0 B. Determine the slope of the