Name Date Class. Negative correlation; each knot decreases the length of the rope

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1 4-5 Reteach Scatter Plots and Trend Lines Correlation is one way to describe the relationship between two sets of data. Positive Correlation Data: As one set increases, the other set increases. Graph: The graph goes up from left to right. Negative Correlation Data: As one set increases, the other set decreases. Graph: The graph goes down from left to right. No Correlation Data: There is no relationship between the sets. Graph: The graph has no pattern. Identify the correlation you would expect to see between the number of grams of fat and the number of calories in different kinds of pizzas. When you increase the amount of fat in a food, you also increase calories. So you would expect to see a positive correlation. Identify the correlation you would expect to see between each pair of data sets. Explain. 1. the number of knots tied in a rope and the length of the rope Negative correlation; each knot decreases the length of the rope 2. the height of a woman and her score on an algebra test No correlation; there is no relationship between height and algebra skill Describe the correlation illustrated by each scatter plot negative correlation positive correlation 38 Holt Algebra 1

2 4-5 Reteach Scatter Plots and Trend Lines (continued) By drawing a trend line over a graph of data, you can make predictions. The scatter plot shows a relationship between a man s height and the length of his femur (thigh bone). Based on this relationship, predict the length of a man s femur if his height is 160 cm. Step 1: Draw a trend line through the points. Step 2: Go from 160 cm on the x-axis up to the line. Step 3: Go from the line left to the y-axis. The point (160, 41) is on the line. Height Femur A man that is 160 cm tall would have a femur about 41 cm long. To find an x-value, go right from the y-value, and then down to the x-value. So, a man with a 42 cm femur would be about 162 cm tall. Your line should have about as many points above it as below it. It may or may not pass through some points. The scatter plot shows a relationship between engine size and city fuel economy for ten automobiles. 5. Draw a trend line on the graph. 6. Based on the relationship, predict... a. the city fuel economy of an automobile with an engine size of 5 L. Possible answer: 8 mi/gal b. the city fuel economy of an automobile with an engine size of 2.8 L. Possible answer: 20 mi/gal c. the engine size of an automobile with a city fuel economy of 11 mi/gal. Possible answer: 4.5 L d. the engine size of an automobile with a city fuel economy of 28 mi/gal. Possible answer: 1.4 L 39 Holt Algebra 1

3 4-5 Scatter Plots and Trend Lines Lesson Objectives Create and interpret scatter plots; Use trend lines to make predictions Vocabulary scatter plot (p. 262): correlation (p. 262): positive correlation (p. 263): negative correlation (p. 263): no correlation (p. 263): trend line (p. 265): 64 Algebra 1

4 4-5 CONTINUED Key Concepts Correlations (p. 263): Positive Correlation Correlations Negative Correlation No Correlation Think and Discuss (p. 265) Get Organized Complete the graphic organizer with either a scatter plot, or a real-world example, or both. Positive Correlation GRAPH EXAMPLE Negative Correlation No Correlation 65 Algebra 1

5 4-5 Practice A Scatter Plots and Trend Lines 1. The table shows the number of soft drinks sold at a small restaurant from 11:00 A.M. to 1:00 P.M. Graph a scatter plot using the given data. The first one has been done for you. Time of Day Number of Drinks 11:00 11:30 12:00 12:30 1: Complete the following. 2. sales go as rainy days increase up 3. gas goes positive: both variables increase negative: one variable increases, other decreases none: points are scattered down as miles increase Write positive, negative, or none to describe the correlation you would expect to see between each pair of data sets. Explain. 4. the temperature during the day and the number of people in the swimming pool positive; as the temperature goes up, more people would go in the pool to cool off 5. the height of algebra students and the number of phone calls they make in one week none; the height of a person has nothing to do with how many phone calls he or she makes 6. The scatter plot at right shows a relationship between the number of batteries needed and the number of toys. Predict how many batteries will be needed for 11 toys. Possible answer: about 38 batteries Holt Algebra 1

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7 4-6 Reteach Arithmetic Sequences An arithmetic sequence is a list of numbers (or terms) with a common difference between each number. After you find the common difference, you can use it to continue the sequence. Determine whether each sequence is an arithmetic sequence. If so, find the common difference and the next three terms. 1, 2, 4, 8, The difference between terms is not constant. This sequence is not an arithmetic sequence. 0, 6, 12, 18, The difference between terms is constant. This sequence is an arithmetic sequence with a common difference of 6. 0, 6, 12, 18, 24, 30, Fill in the blanks with the differences between terms. State whether each sequence is an arithmetic sequence , 12, 10, 8,... Is this an arithmetic sequence? yes 2, 2, , 0.6, 1.0, 1.5,... Is this an arithmetic sequence? no 0.3, 0.4, 0.5 Use the common difference to find the next three terms in each arithmetic sequence. 3. 7, 4, 1, 2, 5, 8, 11, , 0, 5, 10, 15, 20, 25, Determine whether each sequence is an arithmetic sequence. If so, find the common difference and the next three terms. 5. 1, 2, 3, 4,... Find how much you add or subtract to move from term to term. Find how much you add or subtract to move from term to term. Use the difference of 6 to find three more terms. no , 3.75, 6.25, 8.75,... yes; 2.5; 11.25, 13.75, Holt Algebra 1

8 4-6 Reteach Arithmetic Sequences (continued) You can use the first term and common difference of an arithmetic sequence to write a rule in this form: a n a 1 n 1 d any term first term term number common difference After you write the rule, you can use it to find any term in the sequence. Find the 50th term of this arithmetic sequence: 5, 3.8, 2.6, 1.4, First, write the rule. a n a 1 n 1 d a n 5 n Now, use the rule to find the 50th term. Write the general form for the rule. a Substitute the term number. a a a The 50th term is Substitute the first term and common difference. Simplify. Use the first term and common difference to write the rule for each arithmetic sequence. 7. The arithmetic sequence with first term a 1 10 and common difference d , 0, 5, 10,... first term: a 1 5 The first term is 5. The common difference is 1.2. a n 10 n 1 4 common difference: d 5 a n 5 n 1 5 Find the indicated term of each arithmetic sequence. 9. a n 16 n th term: a n 6 n nd term: , 6, 4, 2, th term: Holt Algebra 1

9 4-6 Arithmetic Sequences Lesson Objectives Recognize and extend an arithmetic sequence; Find a given term of an arithmetic sequence Vocabulary sequence (p. 272): term (p. 272): arithmetic sequence (p. 272): common difference (p. 272): Key Concepts Finding the nth Term of an Arithmetic Sequence (p. 273): Finding the nth Term of an Arithmetic Sequence Think and Discuss (p. 274) Get Organized Complete the graphic organizer with steps for finding the nth term of an arithmetic sequence. Finding the n th Term of an Arithmetic Sequence Algebra 1

10 4-6 Practice A Arithmetic Sequences Determine if the sequence is arithmetic. Write yes or no. 1. 5, 9, 14, 20, 2. 10, 22, 34, 46, arithmetic sequence: pattern with common differences no yes Find the common difference for each arithmetic sequence , 15, 18, 21, 4. 30, 24, 18, 12, common difference: same difference from one term to the next 3 6 Find the common difference for each arithmetic sequence. Then find the next three terms , 10, 0, 10, , 98, 96, 94, d 10; 20, 30, 40 d 2; 92, 90, 88 Find the requested term for each arithmetic sequence nd term: a 1 10; d th term: 59, 56, 53, 50, A swim pass costs $30 for the first month. Each month after that, the cost is $20 per month. Riley wants to swim for 12 months. 9. The sequence for this situation is arithmetic. What is the first term of this sequence? What is the common difference? The 12th term will be the amount Riley spends for a one year swim pass. Write the equation for finding the total cost of a one year swim pass. a Holt Algebra 1