Over Lesson 8–8

A. A

B. B

C. C

D. D

Which is an equation for the line passing through the points (1, 1) and (–1, –7)?

Choose the equation in slope-intercept form for the values.

You have already analyzed trends in data displayed in scatter plots. (Lesson 1–6)

• Draw lines of fit for sets of data.

• Use lines of fit to make predictions about data.

• line of fit On a scatter plot, a line drawn that is very close to most of the data points. The line that best fits the data (I think of it as a line that catches “the most fish”).

Make a Prediction from a Line of Fit

Answer:

A. AGRICULTURE The table shows the amount of land in U.S. farms from 1990 to 2005. Graph the data. Make a scatter plot and draw a line of fit for the data.

Graph the data. Draw a line that fits most of the data.

Make a Prediction from a Line of Fit

B. Use the line of fit to predict the amount of land in the year 2015.

Extend the line so that you can estimate the y-value for an x-value of 2015. The y-value for 2015 is about 875 (million).

Answer: So, we can predict that there will be about 875 million acres of land in U.S. farms in 2015.

A. A

B. B

C. C

D. D

HEATING The table shows the heating bill for the month of January for different size houses. Make a scatter plot and draw a line of fit for the data.

A. B.

C. D.

Make Predictions from an Equation

A. INTERNET The scatter plot shows the number of U.S. households (millions) with Internet access. Write an equation in slope-intercept form for the line of fit that is drawn.

Step 1 First, select two points on the line and find the slope. These may or may not be original data points. We have chosen (1995, 10) and (2000, 37).

Make Predictions from an Equation

Definition of slope

(x1, y1) = (1995, 10)(x2, y2) = (2000, 37)

Simplify.

Make Predictions from an Equation

Step 2Use the slope and the coordinates of either point to write the equation of the line in point-slope form.

y – y1 = m(x – x1) Point-slope form

y – 10 = 5.4(x – 1995) Replace (x1, y1) with (1995, 10) and m with

5.4.

Make Predictions from an Equation

Answer: The equation for the line of fit isy = 5.4x – 10,763.

Step 3Solve the point-slope equation for y.

y – 10 = 5.4(x – 1995) Point-slope equation

y – 10 = 5.4x – 10,773 Distributive Property

y = 5.4x – 10,763 Add 10 to each side.

Make Predictions from an Equation

B. Predict the number of U.S. households that will have Internet in the year 2010.

y = 5.4x – 10,763 Write the equation of the line of fit.

y = 5.4(2010) – 10,763 Replace x with 2010.

y = 91Simplify.

Sample answer: 91 million households

A. A

B. B

C. C

D. D

A. TEMPERATURE The scatter plot shows the heating bill for the month of January for different size houses. Write an equation in slope-intercept form for the line of fit drawn. Use the data points (1000, 50) and (3500, 250).

A. y = 0.1x – 50

B. y = 0.08x + 30

C. y = 0.08x – 30

D.

A. A

B. B

C. C

D. D

A. about $256.67

B. about $298.00

C. about $358.00

D. about $360.00

B. Predict the heating bill for a house that is 4100 square feet in size.