SCATTER PLOTS

The scatter plot shows education and income data.

a. Describe the person represented by the point with coordinates (10, 30).This person has 10 years of education and earns $30,000 each year.

b. How many people have exactly 14 years of education? What are their incomes?The points (14, 50), (14, 80), and (14, 90) have education coordinate 14.The three people they represent earn $50,000, $80,000, and $90,000, respectively.

SCATTER PLOTS

Use the table to make a scatter plot of the elevation and

precipitation data.

Atlanta, GA

Boston, MA

Chicago, IL

Honolulu, HI

Miami, FL

Phoenix, AZ

Portland, ME

San Diego, CA

Wichita, KS

Elevation Above

Sea Level (ft)1,050

20

596

18

11

1,072

75

40

1,305

CityMean Annual

Precipitation (in.)51

42

36

22

56

8

44

10

29

SCATTER PLOTS

Use the scatter plot below. Is there a positive correlation, a

negative correlation, or no correlation between

temperatures and amounts of precipitation? Explain.

The values show no relationship.There is no correlation.

PROBLEM SOLVING STRATEGY: SOLVE BY GRAPHING

Use the data in the table below. Suppose this year there are

16 wolves on the island. Predict how many moose are on

the island.Isle Royale Populations

Wolf Moose

14

23

24

22

20

16

700

900

811

1,062

1,025

1,380

Year

1982

1983

1984

1985

1986

1987

Wolf Moose

12

11

15

12

12

13

1,653

1,397

1,216

1,313

1,600

1,880

Year

1988

1989

1990

1991

1992

1993

Wolf Moose

15

16

22

24

14

25

1,800

2,400

1,200

500

700

750

Year

1994

1995

1996

1997

1998

1999

Step 1:  Make a scatter plot by graphing the (wolf, moose) ordered pairs. Use the x-axis for wolves and the y-axis for moose.

Step 2:  Sketch a trend line. The line should be as close as possible to each data point. There should be about as many points above the trend line as below it.

PROBLEM SOLVING STRATEGY: SOLVE BY GRAPHING

(continued)

Look up to find the point on the trend line that corresponds to 16 wolves.

Then look across to the value on the vertical axis, which is about 1,300.

PROBLEM SOLVING STRATEGY: SOLVE BY GRAPHING

(continued)

Step 3:  To predict the number of moose when there are 16 wolves, find 16 along the horizontal axis.

There are about 1,300 moose on the island.

Graph each inequality on a coordinate plane.

GRAPHING LINEAR INEQUALITIES

a. y > 2x + 1

Step 1: Graph the boundary line.Points on the boundary line do not make y > 2x + 1 true. Use a dashed line.

(continued)

GRAPHING LINEAR INEQUALITIES

Step 2: Test a point not on the boundary line.

Test (0, 0) in the inequality.

Since the inequality is false for (0, 0), shade the region that does not contain (0, 0).

y > 2x + 1

0 2(0) + 1 Substitute.

0 0 + 1

0 > 1 false

>

>

(continued)

GRAPHING LINEAR INEQUALITIES

b. y 3x – 2<–

Step 1: Graph the boundary line.Points on the boundary line make y 3x – 2 true. Use a solid line.<–

(continued)

GRAPHING LINEAR INEQUALITIES

Step 2: Test a point not on the boundary line.

Test (3, 0) in the inequality.

Since the inequality is true for (3, 0), shade the region containing (3, 0).

y 3x – 2

0 3(3) – 2 Substitute.

0 9 – 2

0 7 true

<–

<–

<–?

<–?

Cashews cost $2/lb. Pecans cost $4/lb. You plan to spend

no more than $20. How many pounds of each can you buy?

GRAPHING LINEAR INEQUALITIES

Step 1: Write an inequality.

Words cost of cashews

plus cost of pecans

is at most

twenty dollars

Let = number of pounds of pecans.x

+Inequality 2y 4x <– 20

Let = number of pounds of cashews.y

(continued)

GRAPHING LINEAR INEQUALITIES

Step 3:  Graph y = –2x + 10 in Quadrant I since weight is not negative.

Step 2: Write the equation of the boundary line in slope-intercept form.

2y + 4x 20

y –2x + 10

<–

y = –2x + 10

<–

(continued)

GRAPHING LINEAR INEQUALITIES

Step 4: Test (1, 1).

y –2x + 10

1 –2(1) + 10

1 8

The inequality is true. (1, 1) is a solution.

<–<–?

<–

Step 5: Shade the region containing (1, 1).

The graph shows the possible solutions. For example, you could buy 1 pound of pecans and 5 pounds of cashews.

Step 1: Graph y x + 1 on a coordinate plane. Shade in red.

>–

Solve the system y x + 1 and y < 2x + 3 by graphing.

GRAPHING LINEAR INEQUALITIES

>–

Step 2:  Graph y < 2x + 3 on the same coordinate plane. Shade in blue.

(continued)

GRAPHING LINEAR INEQUALITIES

The solutions are the coordinates of all the points in the region that is shaded in both colors.

Check:  See whether the solution (2, 5) makes both of the inequalities true.

y x + 1

5 2 + 1 Replace x with 2 and y with 5.

5 3y The solution checks.

y < 2x + 3

5 2(2) + 3 Replace x with 2 and y with 5.

5 < 7y The solution checks.

>–>–?

>–

<?

Solve the system y = x – 7 and y = 4x + 2 by graphing.

SOLVING SYSTEMS OF LINEAR EQUATIONS

Step 1:  Graph each line.Step 2: Find the point of intersection.

The lines intersect at one point, (–3, –10). The solution is (–3, –10).

y = x – 7

Check:  See whether (–3, –10) makes both equations true.

–10 –3 – 7

–10 = –10

y = 4x + 2

–10 4(–3) + 2

–10 = –10

Replace x with – 3

and y with –10.The solution checks.

Solve each system of equations by graphing.

SOLVING SYSTEMS OF LINEAR EQUATIONS

a. 27x + 9y = 36; y = 4 – 3x b. 8 = 4x + 2y; 2x + y = 5

The lines are the same line.

There are infinitely many solutions.

The lines are parallel.

They do not intersect.

There is no solution.

Find two numbers with a sum of 10 and a

difference of 2.

SOLVING SYSTEMS OF LINEAR EQUATIONS

Step 1: Write equations.

Let x = the greater number.

Let y = the lesser number.

Equation 1 Sum is 10.

x + y = 10Equation 2 Difference is 2.

x – y = 2Step 2: Graph the equations.

The lines intersect at (6, 4).

The numbers are 6 and 4.

(continued)

SOLVING SYSTEMS OF LINEAR EQUATIONS

Check: Since the sum of 6 and 4 is 10 and the difference of 6 and 4 is 2, the answer is correct.