Unit 3

Chapter 1

Ratios and Proportional Relationships

Name ______Class______

Unit Rates

Unit Rate ______

Examples

a. $300 for 6 hours b. 220 miles on 8 gallons c. 24 miles in 4 hours

d. The prices of 3 different bags of dog food are given in the table. Which size bag has the lowest

price per pound rounded to the nearest cent?

e. Tito wants to buy some peanut butter to donate to the local food pantry. Tito wants to buy

as much peanut butter as possible. Which brand should he buy?

f. CD Express offers 4 CDs for $60. Music Place offers 6 CDs for $75. Which store offers the

better buy?

g. After 3.5 hours, Pasha had traveled 217 miles. If she travels at a constant speed, how far

will she have traveled after 4 hours?

h. Write 5 pounds for $2.49 as a unit rate. Round to the nearest hundredth.

Rounding Money

To the nearest penny - ______$12. 467 = $12.47 but $12.464 = $12.46

1. 9.275 ______2. 110.458______3. .751______

4. .3445______5. 2.146______6. 2.1418______

7. 515.497______8. 264.997______9. 1.848______

10. 10.10175______11. 111.119______12. .12511______

13. Quaker Cereal Bars cost $3.79 for 10.4 ounces. How much is she paying per ounce?

14. Fiber One costs $4.99 for 16.2 ounces of cereal. How much is she paying per ounce?

15. Cinnamon Toast Crunch costs $3.89 for 12.8 ounces of cereal. How much is she paying per oz?

16. Multigrain Cheerios cost $4.39 for 9 ounces of cereal. How much is she paying per ounce?

Circle the better buy.

1. 3 batteries for $4.80______12 batteries for $14.76______

2. 22 staplers for $330______4 staplers for $80______

3. 5 calculators for $105______24 calculators for $552______

4. 18 pens for $6.84______30 pens for $8.40______

5. 11 books for $99______29 books for $203______

6. $15.98 for 34 liters of soda______$4.68 for 12 liters of soda______

7. 39 pens for $8.19______11 pens for $3.41______

8. 3 liters of soda for $1.89______10 liters of soda for $6.40______

Complex Fractions

a. 223 b. 613 c. 237 d. 3414

Unit Rate with Fractions

a. Josiah can jog 113 miles in 14 hour. Find his average speed in miles per hour.

b. Tia is painting her house. She paints 2412 square feet in 34 hour. At this rate, how many

square feet can she paint each hour?

c. Mr. Ito is spreading mulch in his yard. He spreads 423 square yards in 2 hours. How many

square yards can he mulch per hour?

d. Aubrey can walk 412 miles in 112 hours. Find her average speed in miles per hour.

e. Pep Club members are making spirit buttons. They make 490 spirit buttons in 3 ½ hours.

Find the number of buttons the Pep Club makes per hour.

f. 1834 g. 364 h. 1314

Proportional Relationships

Two quantities are proportional if ______

Equivalent ratios ______

Examples

a. Andrew earns $18 per hour for mowing lawns. Is the amount of money he earns proportional to the

number of hours he spends mowing? Explain.

b. Uptown Tickets charges $7 per baseball game ticket plus a $3 processing fee per order. Is the cost of

an order proportional to the number of tickets ordered? Explain.

c. You can use the recipe shown to make a fruit punch. Is the amount of sugar used proportional to the

amount of mix used? Explain.

d. At the beginning of the year, Isabel had $120 in the bank. Each week, she deposits another $20. Is

her account balance proportional to the number of weeks of deposits? Use the table below. Explain

your reasoning.

e. The tables shown represent the number of pages Martin and Gabriel read over time. Which

situation represents a proportional relationship between the time spent reading and the number of

pages read? Explain.

Constant of Proportionality – Tables/Graphs

Determine the constant of proportionality for each table. Express your answer as y = kx

Proportional & Non- Proportional Relationships

Days / 0 / 1 / 2 / 3 / 4
Hours of HW / 0 / 4 / 6 / 6 / 14

For the following tables and graphs, if there is a proportional relationship yx=k, write an equation.

a.

X / Y
0 / 0
1 / 5
2 / 10
3 / 15
4 / 20
X / y
0 / 0
4 / 11.5
6 / 16.8
8 / 23
10 / 28

b. c.

d. Use the equation to fill in the tables.

e. The Tortoise can walk ½ a mile in ¼ of an hour. The Hare can run 1 ½ miles in ½ of an hour.

Complete the table for each animal. Graph each animal’s rate in a different color.

What is the Tortoise’s unit rate?

What is the Hare’s unit rate?

Which animal is faster?

Constant Rate of Change

vs.

Proportional Relationship

Straight lines have a ______

Proportional Relationships have ______

a. b. c.

d. e.

f. g.

8. At 2 p.m., the level of the water in the pool was 10 feet. At 6 p.m., the level of water was 2 feet. Find the constant rate of change of the water.

9. JoAnne is depositing money into a bank account. After 3 months there is $150 in the account. After 6 months, there is $300 in the account. Find the constant rate of change of the account.

10. The temperature at noon was 88°F. By 4 P.M., the temperature was 72°F. Find the constant rate of change of the temperature.

Slope

Slope measures the ______

1. 2.

3. 4.

5. 6.

7. GO-KARTS The graph shows the average speed of two go-karts in a race.

What does the point (2, 20) represent on the graph?

What does the point (1, 12) represent on the graph?

What does the slope of each line represent?

Which car is traveling faster?

Direct Variation

1. Which equation is not an example of a direct variation?

a. y=73x+1 b. y=516x c. y=4x d. y=-9x

2. Which equation is not an example of a direct variation?

a. y=x b. 2x+3y=0 c. y=12x d. 5x+6y=30

Name the constant of variations (k) for each equation.

3. y=5x 4. y=12x 5. y=-23x

If y varies directly with x, write an equation for the direct variation. Then find each value

6. If y = 21 when x = 3, find x when y = 42.

7. If y = 36 when x = 4, find y when x = 11.

8. If y = 9 when x = 3/2, find y when x = 2.

Linear Equations

Proportional linear functions can be written in the form ______, where k (m) is the constant of variation, or slope of the line.

The graph represents the cost of Gasoline at $3 per gallon.

Write an equation that represents the cost of gasoline at $3 per gallon and a drink that costs $2.

Non-proportional linear functions can be written in the form ______

This is called the ______.

When an equation is written in this form, m is the ______and b is the ______.

The y-intercept of a line is the y-coordinate of the point where the line crosses the y-axis.

Examples

State the slope and the y-intercept of the graph of each equation

1. y=23x-4 2. y=-5x+3 3. y=14x-6

4. y-2x=5 5. x+y=6 6. y+2=12x

Finding the Slope

Find the slope of the line that passes through the points (-1, 4) and (1, -2)

Find the slope both algebraically and graphically.

1. (0, 2) and (4, 3) 2. (-4, 6) and (5,3)

3. (2, -1) and (7, -1) 4. (-5, 1) and (-4, 7)

Graphing a Line

Graph y=-32x-1 using the slope and y-intercept.

Step 1: Find the slope _____ and y-intercept ______

Step 2: Graph the y-intercept.

Step 3: Use the slope to locate a second point on the line.

Practice

a. y=x+3 b. y=12x-1 c. y=-43x+2

The Student Government is selling spirit T-shirts during spirit week. It costs $20 for the design and $5 to print each shirt. The cost y to print x shirts is given by y=5x+20

Graph the equation to find the number of shirts that can be printed for $50

Step 1 – Plot the point (0,20) to represent the $20 design fee.

Step 2 – Locate another point up 5 and to the right 1.

Step 3 – Connect the points and continue the line through

the rest of the graph to locate the x-coordinate when the

y-coordinate is 50.

Is this a proportional relationship? Why or why not?

Describe what the slope and y-intercept represent.

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