9-3 Linear Functions Going Deeper
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1 Name Class Date 9-3 Linear Functions Going Deeper Essential question: How do ou graph a linear function? 1 CC.8.EE.5 EXPLORE Investigating Change video tutor The U.S. Department of Agriculture defines heav rain as rain that falls at a rate of 1.5 centimeters per hour. A The table shows the total amount of rain that falls in various amounts of time during a heav rain. Complete the table. Time (h) Total Amount of Rain (cm) B Plot the ordered pairs from the table on the coordinate plane at the right. Heav Rainfall C How much rain falls in 3.5 hours? 10 Houghton Mifflin Harcourt Publishing Compan D Plot the point corresponding to 3.5 hours of heav rain. E What do ou notice about all of the points ou plotted? REFLECT Total Amount of Rain (cm) a. Suppose ou continued to plot points for times between those in the table, such as 1. hours or.5 hours. What can ou sa about the locations of these points? Time (h) 3 5 1b. The U.S. Department of Agriculture defines ecessive rain as rain that falls at a rate of centimeters per hour. How do ou think a graph of ecessive rainfall would compare to the graph of heav rainfall? Chapter Lesson 3
2 A linear function is a function whose graph is a nonvertical straight line. The function describing heav rainfall in 1 is a linear function because its graph is a set of points that form a straight line. A linear equation is an equation that represents a linear function. The solutions of a linear equation are ordered pairs that form a straight line on the coordinate plane. CC.8.F.3 EXAMPLE Graphing a Linear Equation Eperts recommend that adult dogs have a dail intake of 50 calories per kilogram of the dog s weight plus 100 calories. Write an equation that gives the recommended number of dail calories for a dog that weighs kilograms. Then show that the equation is a linear equation. Write an equation. Dail calories equals 50 times weight plus 100. = + Complete the table to find some solutions of the equation. Weight (kg), Recommended Dail Intake Calories, 1000 Plot the points, then draw a line through the points to represent all the possible -values and their corresponding -values. The equation is a linear equation because TRY THIS!. Graph the solutions of the linear equation = Then eplain how the graph is different from the graph in the eample.. Number of Calories Weight (kg) Houghton Mifflin Harcourt Publishing Compan - - Chapter 9 35 Lesson 3
3 The linear equation in has the form = m + b, where m and b are real numbers. Ever equation in the form = m + b is a linear equation. Equations that cannot be written in this form are not linear equations. 3 CC.8.F.3 EXAMPLE Determining Whether an Equation is Linear A square tile has a side length of inches. The equation = gives the area of the tile in square inches. Determine whether the equation = is a linear equation. Complete the table. = Side Length, 1 3 Area, Plot the points, then draw a curve through the points to represent all the possible -values and their corresponding -values. Decide whether the equation = a linear equation. Eplain our reasoning Houghton Mifflin Harcourt Publishing Compan REFLECT 3a. How is the equation = different from the linear equations ou have graphed? 3b. Eplain whether ou think the equation = + is a linear equation. 3c. Error Analsis A student graphed several solutions of = - as shown. The student concluded that the equation is not a linear equation. Eplain the student s error Chapter Lesson 3
4 practice Graph solutions of each equation and tell whether the equation is linear or non-linear. 1. = 5 Input, Output,. = Input, Output, Olivia measured several rooms in her house in feet. She wants to epress the measurements in inches. Write an equation relating feet and inches. Tell whether the equation is linear or non-linear. Eplain whether each equation is a linear equation. 5. = 1. = 1. Seth receives $100 from his grandmother for his birthda. He also saves $0 ever month. Write an equation relating months and total savings. Tell whether the equation is linear or non-linear. Houghton Mifflin Harcourt Publishing Compan 7. Error Analsis A student claims that the equation = 7 is not a linear equation because it does not have the form = m + b. Do ou agree or disagree? Wh? Chapter Lesson 3
5 Name Class Date 9-3 Additional Practice Determine whether each function is linear. If so, give the slope and -intercept of the function s graph. 1. f() 3. f() 1 Houghton Mifflin Harcourt Publishing Compan Write a rule for each linear function At the Sweater Store, the price of a sweater is 0% more than the wholesale cost, plus a markup of $8. Find a rule for a linear function that describes the price of sweaters at the Sweater Store. Use it to determine the price of a sweater with a wholesale cost of $.50. Chapter Practice and Problem Solving
6 Problem Solving Write the correct answer. 1. On April 1 15, 191 in Silver Lake, Colorado, 7 inches of snow fell in hours, at an average rate of 3. inches per hour. Find a rule for the linear function that describes the amount of snow after hours at the average rate. 3. The altitude of clouds in feet can be found b multipling the difference between the temperature and the dew point b 8. If the temperature is 75, find a rule for the linear function that describes the height of the clouds with dew point.. At the average rate of snowfall from Eercise 1, how much snow had fallen in 15 hours?. If the temperature is 75 and the dew point is 0, what is the height of the clouds? Houghton Mifflin Harcourt Publishing Compan For Eercises 5 7, refer to the table below, which shows the relationship between the number of times a cricket chirps in a minute and temperature. 5. Find a rule for the linear function that Cricket Chirps/min Temperature ( F) describes the temperature based on, the number of cricket chirps in a 80 0 minute based on temperature. A f() B f() 0 C f() 0 D f() 0. What is the temperature if a cricket chirps 150 times in a minute? F 77.5 F H 130 F G 95 F J 155 F If the temperature is 85 F, how man times will a cricket chirp in a minute? A 1 C 180 B 105 D 00 Houghton Mifflin Harcourt Publishing Compan Chapter 9 30 Practice and Problem Solving
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