Reasoning Algebraically: Different Representations

A forest fire can move at the rate of three meters per second in windy conditions. A fire started by a careless camper has already moved 45 meters. Which is the independent (x) variable?

• Time in seconds

• Distance in meters

Andrea’s dog sleeps 9 hours at night and then takes several 2-hour naps during the daytime. Which is the dependent (y) variable?

• The amount of naps taken

• Total hours slept

Yolanda’s Flower Shop sells long-stem roses for $5 each. In addition, the shop charges a $15 shipping fee.

Which equation represents the total cost, c and flowers purchased, f?

• f = 15c + 5

• f = 5c + 20

• c = 5 + 15f

• c = 5f + 15

Yolanda’s Flower Shop sells long-stem roses for $5 each. In addition, the shop charges a $15 shipping fee. Total cost, c and flowers purchased, f.

Using the equation

c = 5f + 15

What is the cost to purchase a dozen (12) flowers?

• $65

• $75

• $87

• $105

Which scenario matches the equation

y = 3x + 5 ?

• Jimmy walked his dog 3 miles today. Every other day this week he walked his dog 5 miles.

• A movie theater cost $5 for a ticket and $3 for popcorn and a soda

• At a local farm it costs $5 to pick your own basket of apples. It costs $3 for each basket.

At a local farm it costs $5 to pick your own basket of apples. It costs $3 for each basket. Use the equation

c = 5 + 3b to find out how much will 3 baskets cost?

• $9

• $11

• $14

• $18

At a local farm it costs $5 to pick your own basket of apples. It costs $3 for each basket. Use the equation

c = 5 + 3b to find out how much many baskets can be purchased with $35.

• 6 baskets

• 10 baskets

• 12 baskets

• 30 baskets

A submarine is diving at a rate of 0.25 meter per second. Let x represent the time in seconds, and y represent the depth in meters. Which graph could represent this situation?

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A submarine is diving at a rate of 0.25 meter per second. Let x represent the time in seconds, and y represent the depth in meters. Use the graph to estimate where the submarine will be in 16 seconds.

• The submarine will be 4 meters below sea level.

• The submarine will be 8 meters below sea level.

• The submarine will be 10 meters below sea level.

• The submarine will be 16 meters below sea level.

A submarine is diving at a rate of 0.25 meter per second. Let x represent the time in seconds, and y represent the depth in meters. Which equation matches the graph and situation?

• x = -0.25y

• y = 25x

• y = 0.25x

• y = -0.25x