Review for Mastery

[Pages:18]Name _______________________________________ Date __________________ Class __________________

Review for Mastery

Identifying Linear Functions

You can determine if a function is linear by its graph, ordered pairs, or equation.

Identify whether the graph represents a linear function. Step 1: Determine whether the graph is a function.

Every x-value is paired with exactly one y-value; therefore, the graph is a function. Continue to step 2. Step 2: Determine whether the graph is a straight line. Conclusion: Because this graph is a function and a straight line, this graph represents a linear function.

Identify whether {(4, 3), (6, 4), (8, 6)} represents a linear function. Step 1: Write the ordered pairs in a table. Step 2: Find the amount of change in each variable. Determine if the amounts are constant. Conclusion: Although the x-values show a constant change, the y-values do not. Therefore, this set of ordered pairs does not represent a linear function.

Identify whether the function y 5x 2 is a linear function. Try to write the equation in standard form (Ax By C).

y 5x 2 5x 5x 5x y 2

In standard form, x and y ? have exponents of 1 ? are not multiplied together ? are not in denominators, exponents,

or radical signs

Conclusion: Because the function can be written in standard form, (A 5, B 1, C 2), the function is a linear function.

Tell whether each graph, set of ordered pairs, or equation represents a linear function. Write yes or no.

1.

2.

3. x

y

9 5

5 10

1 15

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4. {(3, 5), (2, 8), (1, 12)}

________________________

5. 2y 3x 2

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6. y 4x 7

________________________

________________________

________________________

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Algebra 1

Name _______________________________________ Date __________________ Class __________________

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Algebra 1

Name _______________________________________ Date __________________ Class __________________

Give the domain and range for the graphs below.

7.

8.

9.

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10. Tyler makes $10 per hour at his job. The function f(x) 10x gives the amount of money Tyler makes after x hours. Graph this function and give its domain and range.

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Review for Mastery

Using Intercepts continued

You can find the x- and y-intercepts from an equation. Then you can use the intercepts to graph the equation.

Find the x- and y-intercepts of 4x 2y 8.

To find the x-intercept, substitute 0 for y. 4x 2x 8

4x 2(0) 8 4x 8 4x 8 44 x2

To find the y-intercept, substitute 0 for x.

4x 2y 8 4(0) 2y 8

2y 8 2y 8 22

y 4

The x-intercept is 2.

The y-intercept is 4.

Use the intercepts to graph the line described by 4x 2y 8.

Because the x-intercept is 2, the point (2, 0) is on the graph.

Because the y-intercept is 4, the point (0, 4) is on the graph.

Plot (2, 0) and (0, 4).

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Algebra 1

Name _______________________________________ Date __________________ Class __________________

Draw a line through both points.

Find the x- and y-intercepts.

1.

2.

3.

________________________

________________________

4. The volleyball team is traveling to a game 120 miles away. Their average speed is 40 mi/h. The graphed line describes the distance left to travel at any time during the trip. Find the intercepts. What does each intercept represent?

________________________

__________________________________________________________

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Algebra 1

Name _______________________________________ Date __________________ Class __________________

Use intercepts to graph the line described by each equation.

5. 3x 9y 9

6. 4x 6y 12

7. 2x y 4

Review for Mastery

Rate of Change and Slope

A rate of change is a ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.

The table shows the average retail price of peanut butter from 1986 to 1997. Find the rate of change in cost for each time interval. During which time interval did the cost increase at the greatest rate?

Year

1986

Cost per lb ($) 1.60

1987 1.80

1989 1.81

1992 1.94

1997 1.78

Step 1: Identify independent and dependent variables. Year is independent. Cost is dependent.

Step 2: Find the rates of change.

1986 to 1987 change in cost 1.80 1.60 0.20 0.2 change in years 1987 1986 1

greatest rate of change

1987 to 1989 change in cost 1.81 1.80 0.01 0.005 change in years 1989 1987 2

1989

to 1992

change in cost change in years

1.94 1992

1.81 1989

0.13 3

0.043

1992 to 1997 change in cost 1.78 1.94 0.16 0.032 change in years 1997 1992 5

This rate of change is negative. The price went down during this time period.

The cost increased at the greatest rate from 1986 to 1987.

The table shows the average retail price of cherries from 1986 to 1991. Find the rate of change in cost for each time interval.

Year

1986 1988 1989 1991

Cost per lb ($) 1.27 1.63 1.15 2.26

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Algebra 1

Name _______________________________________ Date __________________ Class __________________

1. 1986 to 1988 change in cost change in years

2. 1988 to 1989 change in cost change in years

3. 1989 to 1991 change in cost change in years

4. Which time interval showed the greatest rate of change? 5. Was the rate of change ever negative? If so, when?

___________________________ ___________________________

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Algebra 1

Name _______________________________________ Date __________________ Class __________________

Find the slope of each line.

6.

7.

8.

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9.

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10.

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11.

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Review for Mastery

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The Slope Formula

You can find the slope of a line from any two ordered pairs. The ordered pairs can be given to you, or you might need to read them from a table or graph.

Find the slope of the line that contains (1, 3) and (2, 0).

Step 1: Name the ordered pairs. (It does not matter which is first and which is second.)

first ordered pair

(1, 3)

(2, 0)

second ordered pair

Step 2: Label each number in the ordered pairs.

(1, 3)

(2, 0)

(x1, y1)

(x2, y2)

Step 3: Substitute the ordered pairs into the slope formula.

m

y2 y1 x2 x1

03 2 (1)

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Algebra 1

Name _______________________________________ Date __________________ Class __________________

3 3

1

The slope of the line that contains (1, 3) and (2, 0) is 1.

Find the slope of each linear relationship.

1.

2.

x

y

4 5

8 3

12 1

16

1

3. The line contains (5, 2) and (7, 6).

________________________

________________________

________________________

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Algebra 1

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