Main Idea and New Vocabulary Example 1: Make Conjectures Lesson Menu
Draw lines of best fit and use them to make predictions about data. line of best fit Main Idea/Vocabulary
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
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
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
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
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
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
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
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 + 110 Replace m with 25 and b with 110. Answer: The equation for the line of best fit is y = 25x + 110. Example 3
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
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
y = 25x + 110 Equation for the line of best fit Make Conjectures The year 2017 is 12 years after 2005. y = 25x + 110 Equation for the line of best fit y = 25(12) + 110 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
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 45F. A. about 25 cups B. about 35 cups C. about 45 cups D. about 99 cups Example 4 CYP