5-7 Scatter Plots and Trend Lines

Quick Review

A scatter plot displays two sets of data as ordered pairs. A trend line for a scatter plot shows the correlation between the two sets of data. The most accurate trend line is the line of best fit. To estimate or predict values on a scatter plot, you can use interpolation or extrapolation.

Example

Estimate the length of the kudzu vine in Week 3.

When w = 3 , l ≈ 10 . w equals 3 comma l almost equal to 10 .  So in Week 3, the length of the kudzu vine was about 10 ft.

Image Long Description

Predict the length of the kudzu vine in Week 11.

l = 3.5 w Use the equation of the trend line . l = 3.5 ( 11 ) Substitute  11  for  w . l = 38.5 Simplify . table with 3 rows and 3 columns , row1 column 1 , l , column 2 equals 3.5 w , column 3 cap usetheequationofthetrendline . . , row2 column 1 , l , column 2 equals 3.5 . open 11 close , column 3 cap substitute . 11 , for , w . , row3 column 1 , l , column 2 equals , 38.5 , column 3 cap simplify , . , end table

The length of the vine in Week 11 will be about 38.5 ft.

Exercises

Describe the type of correlation the scatter plot shows.

32. 
33. 
34. 

35. 1. Make a scatter plot of the data below.

       Heights and Arm Spans

       Height (m)	1.5	1.8	1.7	2.0	1.7	2.1
       Arm Span (m)	1.4	1.7	1.7	1.9	1.6	2.0

    2. Write an equation of a reasonable trend line or use a graphing calculator to find the equation of the line of best fit.
    3. Estimate the arm span of someone who is 1.6 m tall.
    4. Predict the arm span of someone who is 2.2 m tall.

5-8 Graphing Absolute Value Functions

Quick Review

The graph of an absolute value function is a V-shaped graph that opens upward or downward.

A translation shifts a graph either vertically, horizontally, or both. To graph an absolute value function, you can translate y = | x | . y equals vertical line x vertical line .

Example

Graph each function by translating y = | x − 4 | . bold italic y equals vertical line bold italic x minus 4 vertical line .

Start with the graph of y = | x | . y equals vertical line x vertical line .  Translate the graph right 4 units.

Image Long Description

Exercises

Graph the absolute value function y = | x | . bold italic y equals vertical line bold italic x vertical line .

36. y = | x | + 2 y equals vertical line x vertical line plus 2
37. y = | x | − 7 y equals vertical line x vertical line negative 7
38. y = | x + 3 | y equals vertical line x plus 3 vertical line
39. y = | x − 5 | y equals vertical line x minus 5 vertical line

Write an equation for each translation of y = | x | . bold italic y equals vertical line bold italic x vertical line .

40. 5.5 units down
41. 11 units left
42. 13 units up
43. 6.5 units right

44. Write an equation for the absolute value function below.

    

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