What is a solution to both equations? What does it look like? What is the growth pattern? What is the y intercept? CPM Materials modified by Mr.

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1 Common Core Standard: 8.EE.8a What is a solution to both equations? What does it look like? What is the growth pattern? What is the y intercept? CPM Materials modified by Mr. Deyo

2 Title: IM8 Ch When are they the same? Date: Learning Target By the end of the period, I will explain the point of intersection of two graphs. I will demonstrate this by completing Four Square notes and by solving problems in a pair/group activity.

3 Home Work: Sec Desc. Date Due Review & Preview 2 Problems: 5 28, 5 31

5 Vocabulary 1) System of Equations 2) Point of Intersection 3) Equal Values Method 4) Slope Intercept Form

5.2.1 When Are They The Same? In Section 4.1, you graphed lines and curves that represented tile patterns. But what happens when you graph two lines at the same time? What can you learn?

7 5.2.1 When Are They The Same? In Section 4.1, you graphed lines and curves that represented tile patterns. But what happens when you graph two lines at the same time? What can you learn? Today you will use data, graphs, and rules to examine what happens when two lines or curves intersect The Iditarod Trail Sled Dog Race is famous for its incredible length and its use of dogs. The sled drivers, known as mushers, start their dog sleds at Fairbanks, Alaska and ride through the snow for several days until they reach Nome, Alaska. Along the route, there are stations where the competitors check in, so data is kept on the progress of each team. Joyla and her team of dogs have made it through the first five checkpoints. Her buddy Evie left Nome (the finish line) on the day the race started in an effort to meet Joyla and offer encouragement. Evie traveled along the route toward the racers on her snowmobile. The progress of each person is shown on the graph that follows.

8 5 23 Your Task: With your team, analyze the data on the graph. Consider the questions below as you work. Be prepared to defend your results. Which data represents Evie? Which represents Joyla? How can you tell? When did Evie meet Joyla?

9 5 23 Your Task(Continued): With your team, analyze the data on the graph. Consider the questions below as you work. Be prepared to defend your results. How long (distance) was the race? How can you tell? Who traveled faster? Explain how you know. Approximately how long did it take Joyla to finish the race? How did you find your answer?

10 5 24. The point where two lines (or curves) cross is called a point of intersection. Two or more lines (or curves) are called a system of equations. When you work with data, points of intersection can be meaningful, as you saw in the last problem. a) On graph paper, graph y = 3x 4 and y = 2x + 6 on the same set of axes. What is the rule? y = 3x 4 b) Find the point of intersection of these two lines and label the point with its coordinates; that is, write it in the form (x, y). (, ) What is the rule? y = 2x + 6 c) What is the significance of this point for the two rules in part (a)?

11 5 25a The meaning of a point of intersection depends on what the graph is describing. For example, in problem 5 23, the point where Joyla s and Evie s lines cross represents when they met during the race. Examine the graph below and write a brief story that describes the information on the graph. Include a sentence explaining what the point of intersection represents.

12 5 25b The meaning of a point of intersection depends on what the graph is describing. For example, in problem 5 23, the point where Joyla s and Evie s lines cross represents when they met during the race. Examine the graph below and write a brief story that describes the information on the graph. Include a sentence explaining what the point of intersection represents.

13 5 25c The meaning of a point of intersection depends on what the graph is describing. For example, in problem 5 23, the point where Joyla s and Evie s lines cross represents when they met during the race. Examine the graph below and write a brief story that describes the information on the graph. Include a sentence explaining what the point of intersection represents.

14 5 25d The meaning of a point of intersection depends on what the graph is describing. For example, in problem 5 23, the point where Joyla s and Evie s lines cross represents when they met during the race. Examine the graph below and write a brief story that describes the information on the graph. Include a sentence explaining what the point of intersection represents.

15 5 26 LEARNING LOG "Points of Intersection" Date Write your own situation like the ones in problem 5 25 and make a graph. Have two lines or curves that intersect. Explain what is happening in the graph (like in problem 5 25) and what the point of intersection represents in your situation.

16 5 27 To ride to school, Elaine takes 7 minutes to ride 18 blocks. What is her unit rate (blocks per minute)? Assuming she rides at a constant speed, how long should it take her to go 50 blocks? Justify your answer. chapter/ch5/lesson/5.

17 5 28 Gale and Leslie are riding in a friendly 60 mile bike race that started at noon. The graph at right represents their progress so far. chapter/ch5 a) What does the intersection of the two lines represent? b) At approximately what time did Leslie pass Gale? c) About how far had Leslie traveled when she passed Gale? d) What do you think happened to Gale between 1:30 and 3:00? e) If Leslie continues at a steady pace, when will she complete the race?

18 5 29a&b Write an equation (rule) for each of the x y tables below. Then, on one set of axes, use each rule to graph. (Hint: Plot the circled points to figure out the rules from the graph.) chapter/ch5/lesson/5.2.1 What is the rule? y = ( )x + ( ) What is the rule? y = ( )x + ( ) b) Find the point of intersection of these two lines and label the point with its coordinates; that is, write it in the form (x, y). (, ) c) What is the significance of this point for the two rules in part (a)?

19 5 30a,b,c Translate each part below from symbols into words or from words into symbols. chapter/ch5/lesson/5.2.1/pro a) y + 8 b) 2x 48 c) (x + 3) 2

20 5 30d,e,f d) Translate each part below from symbols into words or from words into symbols. The opposite of six times the square of a number. chapter/ch5/lesson/5.2.1/prob e) A number multiplied by itself, then added to five. f)* The opposite of six times a number, then added to five.

21 5 31a&b Solve each of the following equations for the indicated variable. Show all of your steps. Then check each solution. a) Solve for x b) Solve for w y = 2x 5 p = 3w chapter/ch5/lesson/5.2

22 5 31c&d Solve each of the following equations for the indicated variable. Show all of your steps. Then check each solution. c) Solve for m d) Solve for y 2m 6 = 4n + 4 3x y = 2y chapter/ch5/lesson/5.2

Is there a different way to get the same result? Did we give enough information? How can we describe the position? CPM Materials modified by Mr.

Common Core Standard: 8.G.3 Is there a different way to get the same result? Did we give enough information? How can we describe the position? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 6.2.1 What