Lesson 2
Two Equations for Each Relationship
Let’s investigate the equations that represent proportional relationships.
Problem 1
The table represents the relationship between a length measured in meters and the same length measured in kilometers.
- Complete the table.
- 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 | |
| \(x\) |
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 \(b =\).
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.
- How much does the nylon rope cost per meter?
- How long is a piece of nylon rope that costs $1.00?
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: \(y =\)
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.