2. Main Idea and New Vocabulary Example 1: Make Conjectures
Lesson Menu

3. Draw lines of best fit and use them to make predictions about data.
line of best fit
Main Idea/Vocabulary

4. Make Conjectures
ZOOS Refer to the information in the table below. Construct a scatter plot using the data. Then draw a line that seems to best represent the data.
Example 1

5. Graph each of the data points. Draw a line that fits the data.
Make Conjectures
Graph each of the data points. Draw a line that fits the data.
Answer:
Example 1

6. ALLIGATORS Refer to the information in the table below
ALLIGATORS Refer to the information in the table below. Construct a scatter plot using the data. Then draw a line that seems to best represent the data.
A. C.
B. D.
Example 1 CYP

7. The y-value for 33 is about 67.
Make Conjectures
ZOOS Refer to the scatter plot below. Use the line of best fit to make a conjecture about the maximum longevity for an animal with an average longevity of 33 years.
The y-value for 33 is about 67.
Answer: We can predict that the maximum longevity for an animal with an average longevity of 33 years is about 67 years.
Example 2

8. ALLIGATORS Refer to the scatter plot below
ALLIGATORS Refer to the scatter plot below. Use the line of best fit to make a conjecture about the body length of an alligator that has a tail length of 2 feet.
A. 1 foot
B. 2 feet
C. 4 feet
D. 8 feet
Example 2 CYP

9. Make Conjectures
FRUIT The scatter plot shows the number of new foods claiming to be high in fruit. Write an equation in slope-intercept form for the line of best fit that is drawn.
Example 3

10. Make Conjectures
Choose any two points on the line. They may or may not be data points. The line passes through points (5, 250) and (7, 300). Use these points to find the slope, or rate of change, of the line.
Definition of slope
(x1, y1) = (5, 250) and (x2, y2) = (7,300)
The slope is 25.
Example 3

11. y = mx + b Slope-intercept form
Make Conjectures
The y-intercept is 110 because the line of fit crosses the y-axis at about the point (0, 110).
y = mx + b Slope-intercept form
y = 25x Replace m with 25 and b with 110.
Answer: The equation for the line of best fit is y = 25x
Example 3

12. HOT CHOCOLATE The scatter plot shows cups of hot chocolate sold at a concession stand and the outside temperature. Write an equation in slope-intercept form for the line of best fit that is drawn. Use the points (10, 60) and (60, 25).
A. y = 0.7x + 60
B. y = 0.7x + 67
C. y = –0.7x + 60
D. y = –0.7x + 67
Example 3 CYP

13. Make Conjectures
FRUIT The scatter plot shows the number of new foods claiming to be high in fruit. Use the equation for the line of best fit, y = 25x + 110, to make a conjecture about the number of new foods that will claim to be high in fruit in 2017.
Example 4

14. y = 25x + 110 Equation for the line of best fit
Make Conjectures
The year 2017 is 12 years after 2005.
y = 25x Equation for the line of best fit
y = 25(12) Replace x with 12.
y = 410 Simplify.
Answer: In 2017, there will be about 410 new foods that will claim to be high in fruit.
Example 4

15. HOT CHOCOLATE The scatter plot shows cups of hot chocolate sold at a concession stand and the outside temperature. Use the equation for the line of best fit, y = –0.7x + 67, to make a conjecture about the cups of hot chocolate sold when the outside temperature is 45F.
A. about 25 cups
B. about 35 cups
C. about 45 cups
D. about 99 cups
Example 4 CYP