Main Idea and New Vocabulary

Example 1: Make Conjectures

Example 2: Make Conjectures

Example 3: Make Conjectures

Example 4: Make Conjectures

• Draw lines of best fit and use them to make predictions about data.

• line of best fit

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.

Graph each of the data points. Draw a line that fits the data.

Make Conjectures

Answer:

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.

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.

Make Conjectures

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.

A. 1 foot

B. 2 feet

C. 4 feet

D. 8 feet

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.

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.

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.

Make Conjectures

Definition of slope

(x1, y1) = (5, 250) and (x2, y2) = (7,300)

The slope is 25.

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.

Make Conjectures

Answer: The equation for the line of best fit isy = 25x + 110.

A. y = 0.7x + 60

B. y = 0.7x + 67

C. y = –0.7x + 60

D. y = –0.7x + 67

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).

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.

Make Conjectures

The year 2017 is 12 years after 2005.

y = 25x + 110 Equation for the line ofbest fit

y = 25(12) + 110 Replace x with 12.

y = 410 Simplify.

Make Conjectures

Answer: In 2017, there will be about 410 new foodsthat will claim to be high in fruit.

A. about 25 cups

B. about 35 cups

C. about 45 cups

D. about 99 cups

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.