Unit 2 Introducing Proportional Relationships

Which graph represents a proportional relationship?

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Answer explanation

The graph should be a straight line through the origin (0,0).

Tags

CCSS.7.RP.A.2

The graph shows the cost C in dollars of w pounds of blueberries, a proportional relationship.

Select all the true statements.

• 1 pound of blueberries costs $2.75

• 2.75 pounds of blueberries cost $1

• 5 pounds of blueberries cost $15.50

• 12 pounds of blueberries cost $33

• The point (3,9) is on the graph of the proportional relationship

Answer explanation

Find the unit rate (cost of one pound) and/or use a table. TWO statements are correct.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.SSE.A.1

Andre rode his bike at a constant speed. He rode 1 mile in 5 minutes. Which of these equations represents the amount of time t (in minutes) that it takes him to ride a distance of d miles?

• $t=5d$

• $t=\frac{1}{5}d$

• $t=d+4$

• $t=d-4$

Answer explanation

The amount of time traveled is proportional to the distance. Multiply distance by pace (in miles per minute) to get total time.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

The two lines represent the amount of water, over time, in two tanks that are the same size. Which container is filling more quickly?

• Container A is filling more quickly

• Container B is filling more quickly

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSS.ID.C.7

Explain how you know which container is filling more quickly.

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Answer explanation

The container that is filling more quickly is the one for which the graph is steeper.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSS.ID.C.7

The table shows the weights of apples at a grocery store. Complete the RED box (weight of 2 apples) so that there is a proportional relationship between the number of apples and their weight.

Give the NUMBER ONLY, no units.

Answer explanation

To start, find the weight of ONE apple. This is your unit rate; it is also your constant of proportionality.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

The table shows the weights of apples at a grocery store. Complete the BLUE box (weight of 12 apples) so that there is a proportional relationship between the number of apples and their weight.

Give the NUMBER ONLY, no units.

Answer explanation

To start, find the weight of ONE apple. This is your unit rate; it is also your constant of proportionality.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

CCSS.6.RP.A.3

 $F=\frac{9}{5}C+32$  

The equation above relates temperature measured in degrees Celsius, C, to degrees Fahrenheit, F. Determine whether there is a proportional relationship between C and F.

• Yes, the relationship between C and F is proportional.

• No, the relationship between C and F is not proportional.

Tags

CCSS.HSA.SSE.A.1

 $F=\frac{9}{5}C+32$  

Explain your reasoning for the previous question.

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Answer explanation

Consider the graph of the equation and/or a table relating values of C and F. Consider also the standard equation for proportional relationships: y=kx

A recipe for salad dressing calls for 3 tablespoons of oil for every 2 tablespoons of vinegar. The line represents the relationship between the amount of oil and the amount of vinegar needed to make salad dressing according to this recipe. The point (1, 1.5) is on the line.

Label the horizontal axis (RED box).

• Oil (tablespoons)

• Vinegar (tablespoons)

Tags

CCSS.HSA.CED.A.2