Lesson 2

Two Equations for Each Relationship

Problem 1

The table represents the relationship between a length measured in meters and the same length measured in kilometers. 

  1. Complete the table.
  2. Write an equation for converting the number of meters to kilometers. Use x for number of meters and y for number of kilometers.
meters kilometers
1,000 1
3,500
500
75
1
x

Solution

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Problem 2

Concrete building blocks weigh 28 pounds each. Using b for the number of concrete blocks and w for the weight, write two equations that relate the two variables. One equation should begin with w = and the other should begin with b =.

Solution

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Problem 3

A store sells rope by the meter. The equation p = 0.8L represents the price p (in dollars) of a piece of nylon rope that is L meters long.

  1. How much does the nylon rope cost per meter?
  2. How long is a piece of nylon rope that costs $1.00?

Solution

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Problem 4

The table represents a proportional relationship. Find the constant of proportionality and write an equation to represent the relationship.

a y
2 \frac23
3 1
10 \frac{10}{3}
12 4

Constant of proportionality: __________

Equation: y =

Solution

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(From Unit 5, Lesson 1.)

Problem 5

Jada walks at a speed of 3 miles per hour. Elena walks at a speed of 2.8 miles per hour. If they both begin walking along a walking trail at the same time, how much farther will Jada walk after 3 hours? Explain your reasoning.

Solution

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(From Unit 2, Lesson 18.)