GASOLINE The graph represents the cost of gasoline at $3 per gallon.

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1 9-6 Slope-Intercept Form MAIN IDEA Graph linear equations using the slope and -intercept. New Vocabular slope-intercept form -intercept Math Online glencoe.com Etra Eamples Personal Tutor Self-Check Quiz GASOLINE The graph represents the cost of gasoline at $ per gallon.. Write an equation that represents the cost of gasoline at $ per gallon and a drink that costs $.. Graph the equation from Eercise. Cost ($) Gasoline 6 5 = Number of Gallons Proportional linear functions can be written in the form = k, where k is the constant of variation, or slope of the line. Nonproportional linear functions can be written in the form = m + b. This is called the slope-intercept form. When an equation is written in this form, m is the slope and b is the -intercept. The -intercept of a line is the -coordinate of the point where the line crosses the -ais. Find Slopes and -intercepts of Graphs State the slope and the -intercept of the graph of each equation. = _ - _ = + (-) Write the equation in the form = m + b. = m + b _ m =, b = - The slope of the graph is _, and the -intercept is -. + = 6 + = = 6 - = 6 - Write the original equation. Subtract from each side. Simplif. = Write the equation in the form = m + b. Recall that - means -. = m + b m = -, b = 6 The slope of the graph is -, and the -intercept is 6. a. = -5 + b. = _ - 6 c. - = 5 Lesson 9-6 Slope-Intercept Form 95

2 Check for Accurac To check our graph, substitute the - and -values of another point on our graph into the equation. For Eample, test the point (, -). = - _ - - = - _ () - - = = - Graph = - _ Graph Using Slope-Intercept Form - using the slope and -intercept. Step Find the slope and -intercept. = - _ - _ slope = -, -intercept = - Step Graph the -intercept -. Step Write the slope - _ as _-. Use it to locate a second point on the line. m = _ - change in : down units change in : right units Step Draw a line through the two points. down units O right units Graph each equation. d. = + e. = _ - f. = - _ + Graph an Equation to Solve Problems ACTIVITIES The Student Council is selling spirit T-shirts during spirit week. It costs $0 for the design and $5 to print each shirt. The cost to print shirts is given b = Graph the equation to find the number of shirts that can be printed for $50. = slope = 5, -intercept = 0 Plot the point (0, 0). Locate another point up 5 and right. Draw the line. The -coordinate is 6 when the -coordinate is 50, so the number of T-shirts is (, 5) 0 (0, 0) Real-World Link Shirt designs can be created on a computer then sent to a compan to screen print the shirts. Each color requires a separate screen for the ink to pass through. 5 Describe what the slope and -intercept represent. The slope 5 represents the cost in dollars per T-shirt, and the -intercept 0 is the one-time charge in dollars for preparing the design. 6 Is the total cost proportional to the number of T-shirts? Eplain. Compare the ratio of total cost to number of T-shirts for two points. _ 5 = $5 per T-shirt _ 50 $8. per T-shirt The ratios are different. 6 So, the total cost is not proportional to the number of T-shirts. TRANSPORTATION A tai fare can be determined b the equation = , where is the number of miles traveled. g. Graph the equation to find the cost of traveling 8 miles. h. What do the slope and -intercept represent? i. Is the total fare proportional to the number of miles? Eplain. 96 Chapter 9 Algebra: Linear Functions

3 Eamples, (p. 95) Eample (p. 96) Eamples 6 (p. 96) State the slope and the -intercept for the graph of each equation.. = +. = - _ 6 - _. + = Graph each equation using the slope and the -intercept.. = _ - 5. = - 5_ + 6. = SCHOOL For Eercises 7 9, use the following information. Liam is reading a 5-page book for school. He can read 0 pages in one hour. The equation for the number of pages he has left to read is = 5-0, where is the number of hours he reads. 7. Graph the equation to find how man pages Liam has left to read after hours. 8. What do the slope and -intercept represent? 9. Is the number of pages left to read proportional to the time read? Eplain. HOMEWORK HELP For Eercises HELP See Eamples, 6 State the slope and the -intercept for the graph of each equation. 0. = +. = = _ - 6. = - _ 7 - _. - = = - 7 Graph each equation using the slope and the -intercept. 6. = _ = - + _ 8. = - _ + 9. = _ = = - BOATING For Eercises, use the following information. The Lakeside Marina charges a $5 rental fee for a boat, in addition to charging $5 an hour for usage. The total cost of renting a boat for hours can be represented b the equation = Graph the equation to find the total cost for a -hour rental.. What do the slope and the -intercept represent?. Is the total cost proportional to the number of hours? Eplain. TRAVEL For Eercises 5 7, use the following information. The Viera famil is traveling from Philadelphia, Pennslvania, to Orlando, Florida, for vacation. The equation =, represents the distance remaining in their trip after hours. 5. Graph the equation to find the distance remaining after 6 hours. 6. What do the slope and -intercept represent? 7. Is the distance remaining proportional to the hours driven? Eplain. Lesson 9-6 Slope-Intercept Form 97

4 8. INSECTS The equation = can be used to approimate the temperature in degrees Fahrenheit based on the number of chirps a cricket makes in 5 seconds. Graph the equation to estimate the number of chirps a cricket will make in 5 seconds if the temperature is 80 F. GEOMETRY For Eercises 9, use the supplementar angles at the right. 9. Write the equation in slope-intercept form. 0. Graph the equation. + = 80. Is the relationship between supplementar angles proportional? Eplain our reasoning. For Eercises 5, use the graph at the right.. What is the slope and -intercept of the line?. Describe how the slope and -intercept appear on the graph.. Use the slope and -intercept to write the equation of the line in slope-intercept form. 5. The -intercept of a line is the -coordinate of the point where the line crosses the -ais. What are the coordinates of the - and -intercepts? O WEATHER For Eercises 6 8, use the following information. The equation =.5 + can be used to find the total rainfall in inches hours after :00 p.m. during a tropical storm. 6. What is the slope and -intercept of the line? 7. Describe how the slope and -intercept appear on the graph of the equation. Then eplain their meaning. 8. What are the coordinates of the - and -intercepts? PRACTICE EXTRA PRACTICE See pages 69, 708. For Eercises 9 and 0, complete parts a d for each table. The points given in the table lie on a line. a. Find the slope and -intercept of the line. b. Describe how the slope and -intercept appear on the graph of the line. c. Use the slope and -intercept to find the equation of the line in slopeintercept form. d. Find the coordinates of the - and -intercepts H.O.T. Problems. OPEN ENDED Draw the graph of a line that has a -intercept but no -intercept. What is the slope of the line? 98 Chapter 9 Algebra: Linear Functions

5 . CHALLENGE A triangle s original vertices are located at (, 0), (, -), and (, -). The triangle is translated unit to the right and units up. It is then reflected across the graph of = +. Determine the new vertices of the triangle.. REASONING What is the slope and -intercept of a vertical line? WRITING IN. MATH Write a real-world problem that involves a linear relationship. Describe how the slope and -intercept would appear in these three different representations of the problem: table, equation, and graph. 5. Which best represents the graph of = +? A B --O O C D ---O O Which statement could be true for the graph below? Total Earnings Sales (thousands of dollars) F Mr. Blackwell will earn $,750 if his sales are $0,000. G Ms. Chu will not earn an mone if she has no sales. H Mr. Montoa earns $50 for ever $,000 he sells. J Ms. James earns $,500 if she sells $,500 worth of merchandise. 7. BICYCLING Angel rides her bike 5 miles in _ hours. How long will it take her to ride 60 miles? (Lesson 9-5) Find the slope of the line that passes through each pair of points. (Lesson 9-) 8. M(, ), N(-, ) 9. S(-5, ), T(-7, ) 50. X(-9, 5), Y(-, 5) 5. MEASUREMENT The function = 0.9 approimates the number of centimeters in inches. Make a function table. Then graph the function. (Lesson 9-) PREREQUISITE SKILL Solve each equation. Check our solution. (Lesson 8-) 5. a - = = -n _ p - 7 = _ 5 = 0 Lesson 9-6 Slope-Intercept Form 99