Find four solutions of. Choose four values for x. Then substitute each value into the equation to...

Find four solutions of .

Choose four values for x. Then substitute each value into the

equation to solve for y. There are many possible solutions.

The solutions you find depend on which x values you choose.

Graphing Functions with Ordered Graphing Functions with Ordered PairsPairs

2

3

2

1

0

x (x, y)y

9 (0, 9)

7 (1, 7) 5 (2, 5)

3 (3, 3)

Sample Answer: (0, 9), (1, 7), (2, 5), and (3, 3)

Choose four x values and substitute them into

If 0 is the inputinput 9 is the

outputoutput.If 1 is the inputinput 7 is the

outputoutput.If 2 is the inputinput 5 is the

outputoutput.If 3 is the inputinput 3 is the

outputoutput.

Graphing Functions with Ordered Graphing Functions with Ordered PairsPairs

33

4

Graph by plotting ordered pairs.

First, find ordered pair solutions.

2

1

0

–1

x

(x, y)y

–4 (–1, –4)–3 (0, –3)–2 (1, –2)–1 (2, –1)

Four solutions are (–1,–4), (0,–3), (1,–2), and (2,–1).

Graphing Functions with Ordered Graphing Functions with Ordered PairsPairs

5

6

Coordinate Plane Coordinate Plane

7

Graphing Functions with Ordered Graphing Functions with Ordered PairsPairs Plot these ordered pairs and draw a line through them.

Now, draw a straight line between the points

Extend your line well beyond the two points.

Finally, check either of your last two points.

Is it on your line?

Then, you’ve graphed correctly!

Plot 2 points.

8

Four solutions are (–1,–4), (0,–3), (1,–2), and (2,–1).

9

Answer:

Graph y = 5 – x by plotting ordered pairs.

Graphing Functions with Ordered Graphing Functions with Ordered PairsPairs

10

1. State the x-intercept and the y-intercept of the line.

The graph crosses the x-axis at (–2,

0). The x-intercept is –2. The graph

crosses the y-axis at (0, –2). The y-

intercept is –2.Answer: –2; –2

Graphing Functions with Graphing Functions with xyxy InterceptsIntercepts

11

2. State the x-intercept and the y-intercept of the line.

The graph does not cross the x-axis. There is no x-intercept.

The graph crosses the y-axis

at (0, 2). The y-intercept is 2.

Answer: none; 2

Answer: –1; none

State the x-intercept and the y-intercept of each line.

Answer: 1; 3

Graphing Functions with Graphing Functions with xyxy InterceptsIntercepts

12

.

.

Write the equation.

Simplify.

Replace y with 0.

The x-intercept is 4. So, the graph crosses the x-axis at

(4, 0).

Graphing Functions with Graphing Functions with xyxy InterceptsIntercepts

13

5.Find the x-intercept and the y-intercept for the graph of

To find the x-intercept, let

The y-intercept is 2. So, the graph crosses the y-axis at (0,

2).

Answer: x-intercept, 4; y-intercept, 2

Write the equation.

Replace x with 0.

Simplify.

Divide each side by 2.

Graphing Functions with Graphing Functions with xyxy InterceptsIntercepts

14

5. To find the y-intercept, let .

Step 1 Find the x-intercept. Write the equation.

Replace y with 0.

Add 6 to each side.

Divide each side by 3.

The x-intercept is 2, so the graph passes through

(2, 0).

Graphing Functions with Graphing Functions with xyxy InterceptsIntercepts

15

7. Graph using the x- and y-intercepts.

Step 2 Find the y-intercept.

The y-intercept is –6, so the graph passes through

(0, –6).

Write the equation.

Replace x with 0.

Simplify.

Check Choose some other point on the line and determine whether its ordered pair is a solution of

The y-intercept is –6,

so the graph passes

through (0, –6).

7. The x-intercept is

2. So, the graph

crosses the x-axis

at (2, 0).

Draw your line.

Graphing Functions with Graphing Functions with xyxy InterceptsIntercepts

16

17

8. Graph using the x- and y-intercepts.

Graphing Functions with Graphing Functions with xyxy InterceptsIntercepts

18

9. Mrs. Jones has $300 for home repairs. A plumber charges her

$50 an hour. The equation represents the amount of money left in her budget after x number of plumbing hours.Use the intercepts to graph the equation.Step 1 Find the x-intercept.

Write the equation.

Replace y with 0.

Divide each side by –50.

The x-intercept is

6.

Graphing Functions with Graphing Functions with xyxy InterceptsIntercepts

19

Subtract

300 from each side.

9. Step 2 Find the y-intercept.

The y-intercept is 300.

Write the equation.

Replace x with 0.

Reread the problem. Since Reread the problem. Since the x-intercept is 6, what does the x-intercept is 6, what does

that actually mean?that actually mean?

The y-intercept is 300. What The y-intercept is 300. What does that actually mean?does that actually mean?

(6, 0)

(0, 300)

Graphing Functions with Graphing Functions with xyxy InterceptsIntercepts

20

9. Answer: Describe what the intercepts mean.

Answer: The y-

intercept shows how

much money Mrs.

Jones has in her

budget before any

work is done. The x-

intercept means that

she can afford only 6

hours of plumbing

repair.

10. Suzanne has $125 to spend on new shoes. The shoe store is having a sale in which every pair of shoes is priced at $25. The equation

represents the amount of money Suzanne has left after purchasing x pairs of shoes.

Use the intercepts to graph the equation.

Answer:

Graphing Functions with Graphing Functions with xyxy InterceptsIntercepts

21

10. Describe what the intercepts mean.

Answer: The y-intercept shows how much money Suzanne has

before buying any shoes. The x-intercept means that she can

afford only 5 pairs of shoes.

Graph using the x- and y-intercepts.

The y-intercept is –4, and there is no x-intercept.

Answer:

Note that is the same as

Graphing Functions with Graphing Functions with xyxy InterceptsIntercepts

22

11.11.

The x-intercept is 5, and there is no y-intercept.

Graph using the x- and y-intercepts.

Answer:

Note that is the same as

Graphing Functions with Graphing Functions with xyxy InterceptsIntercepts

23

12.12.

Graph each equation using the x- and y-intercepts.

13. 14.

Answer: Answer:

Graphing Functions with Graphing Functions with xyxy InterceptsIntercepts

24

25

Make Your Own FunctionMake Your Own FunctionRewrite your data in set notation*

* Set notation lists data as ordered pairs.

* Example: { (2,8), (-8,7), (0,4) }

~ What is the independent variable?

~ Write only the domain of the data in set notation.

~ What is the dependent variable?

~ Write only the range of the data in set notation.

~ Does the data represent a function?

* Explain your answer.

'

26

Make Your Own FunctionMake Your Own FunctionPlot all ordered pairs, then connect each point from left to right.

~ When the line crosses the x-axis, what's the value of y?

~ What's the x-intercept?

~ When the line crosses the y-axis, what's the value of y?

~ What's the y-intercept?

~ What does the x-intercept mean?

~ What does the y-intercept mean?

27

Coordinate Plane Coordinate Plane

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Coordinate Plane Coordinate Plane