Unit 3 Linear Relationships

There are many cylinders with a height of 5 inches. Let r represent the radius in inches and V represent the volume in cubic inches.

Complete the table relating the radius and volume of cylinders with height 5 inches. Write each volume as a multiple of , or round to the nearest cubic inch.

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

There are many cylinders with a height of 5 inches. Let r represent the radius in inches and V represent the volume in cubic inches. Is there a linear relationship between the radius and the volume of these cylinders? Explain how you know.

• No, because the 3 points are not on the same line. The slope between r = 1 and r = 2 is 47 and the slope between r = 2 and r = 3 is 78

• Yes, because the 3 points are on the same line. The slope between r = 1 and r = 2 is 47 and the slope between r = 2 and r = 3 is 47

Tags

CCSS.HSF-LE.A.1B

There are many cylinders with a height of 5 inches. Let r represent the radius in inches and V represent the volume in cubic inches.

If a cylinder with height 5 inches and radius r is filled with water, it can fill a certain pitcher. How many of these pitchers can a cylinder with height 5 inches and radius 2r fill? Explain how you know.

• 2 Pitchers because if you double the radius of a cylinder, the volume also gets doubled.

• 4 Pitchers because if you double the radius of a cylinder the volume gets quadrupled.

• 6 Pitchers because if you double the radius of a cylinder the volume gets quadrupled and 2 + 4 = 6.

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

For cones with radius 9 units, the equation V=27πh relates the height h of the cone, in units, and the volume V of the cone, in cubic units.

Here is the sketch of the graph.

Is there a linear relationship between height and volume? Explain how you know.

• No, there is not a linear relationship. The graph is curved, not straight.

• Yes, there is a linear relationship because all proportional relationships are linear.

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CCSS.HSF-LE.A.1B

Clare owns a mobile pet grooming company. She charges $20 to come to your home plus $30 per hour to groom your pet. Which equation models the amount she charges over time?

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

The graph shows the cost of a personal pizza (y) vs. the number of toppings (x). Which equation best describes the relationship above?

• y = 2x

• y = 2x + 4

• y = 4x

• y = 2x + 2

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CCSS.8.EE.B.5

An electrician charges $25 to make a house call, plus $40 for every hour of work. Which equation shows how to find C, the total cost for having the electrician work for h hours?

• C = 25 + 40h

• C = 65 + h

• C= 65h

• C = 25h + 40

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Which of the following situations could be described by the equation y = 120 - 25x ?

• There are 120 people in the football stadium, and 25 more are entering each hour

• A plumber charges $25 for a house call and $120 per hour

• A teacher has 120 students. Her third period has 25 students

• There are 120 gallons of water in a tank. It releases water at a rate of 25 gallons per minute

Pierre sells homecoming mums for $10, plus and additional $0.75 per decoration added. Which table shows the relationship between the total cost of the mum (C) and the number of decorations (d)?

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Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Which graph shows the equation y = -1/2x + 5

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