Unit 5-Part B Test

Chapter 1Lessons 4-9

1-4

• Two quantities are proportional if they have a constant ratio or unit rate

• For relationships in which this ratio is not constant, the two quantities are nonproportional

• Use a table to see if quantities are proportional, show your work by writing ratios, and explain your reasoning

1-4

• Jess walks 6.5 miles every 2 days. Is the number of miles she walks proportional to the number of days she walks? Complete the table and explain your reasoning.

Days 2 4 6

Miles Walked

1-4

• Which situation best represents a proportional relationship? Show proof and explain your reasoning.

a. Jenny sold 3 necklaces for $9 and 4 necklaces for $11b. Jim biked 4 miles in 20 minutes and 6 miles in 30

minutesc. Larry packed 24 dishes in 6 boxes and 54 dishes in 9

boxesd. Alice put 16 pieces of candy in 2 bags and 30 pieces of

candy in 4 bags

1-5

• Identify Proportional Relationships from a Graph– It must be a straight line– It must pass through the origin*Must have equal ratios

• Units of Time = x-axis• Money = y-axis

1-5

• Does the graph show a proportional relationship? Explain.

1-5

• Determine whether the relationship between the two quantities shown in the table are proportional by graphing on the coordinate plane. Explain your reasoning. (half sheet)

Temperature (Degrees)Celsius Fahrenheit

0 325 41

10 5015 5920 68

1-6

• Solve proportions by finding the cross products (multiply diagonals)

• = ad = bc

1-6

• Do they form a proportion?

1-6

• Problem Solving Using Proportions– Figure out the 2 quantities we are comparing by

looking at the question—set up a units only fraction– Use the information in the problem to set up the 1st

fraction. Line up units going across– For the 2nd fraction, put variable for what we are trying

to find and get other value from question part of the problem

– Solve using cross products and label answer

1-6

Write and solve by using a proportion.• Fifteen scoops of lemonade drink mix are

needed to make five gallons. How many gallons will 6 scoops of lemonade mix make?

1-6

Write and solve by using a proportion.• To determine the number of deer in a forest, a

forest ranger tags 280 and releases them back into the forest. Later, 405 deer are caught, out of which 45 of them are tagged. Predict how many deer are in the forest.

1-6

• A pond is being dug according to plans that have a scale of 1 inch = 6.5 feet. The maximum distance across the pond is 9.75 inches on the plans. What will be the actual maximum distance across the pond?

1-6

• The table shows the amount of calories in various servings of a specific brand of yogurt.

• If the rate of calories per serving remains the same, how many calories would complete the table?

Calories per Serving2 220.45 5519 ?

1-7

• Constant Rate of Change

– Simplify to a unit rate with labels*Focus on numbers that have the same unit

1-7

• Use a Table

The table shows the number of miles Claire drove on a trip. What is the constant rate of change?

Time (hours)

2 4 6

Distance (miles)

130 260 390

1-7

• Use a Graph• Find the constant rate of change

1-7

• Jaime and Ryan work at the grocery store. The wages earned for the weekend are shown in the table and graph. Who gets paid more per hour? Explain.

1-8

• Slope = constant rate of change– Can be found in 3 different ways , , formula– Explain what slope represents by discussing y-

value first and x-value second

1-8

• The table shows the number of packages of raisins per box. Graph the data. Then find the slope of the line and explain what it represents. (half sheet)

Boxes 1 2 3 4

Packages 20 40 60 80

1-8

• 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? • Find the slope of each line.

What does the slope of each line represent?

• Which car is traveling faster? How do you know?

1-9

• Direct Variation—a linear relationship is a direct variation when the ratio of y to x is a constant, k. We say y varies directly with x.– Proportional relationship– K=constant rate of change or slope– y = kx

1-9

• Determine whether the relationship is a direct variation. If so, state the constant of proportionality.

Days, x 2 4 6 8Hours

worked, y

16 32 54 72

1-9

• A photographer charges a $30 sitting fee and then $6 for each photograph ordered. Make a table and a graph to show the cost of 1, 2, 3, and 4 photographs. Is there a direct variation? Explain.