Lesson 4

Proportional Relationships and Equations

Let’s write equations describing proportional relationships.

Problem 1

A certain ceiling is made up of tiles. Every square meter of ceiling requires 10.75 tiles. Fill in the table with the missing values.

square meters of ceiling number of tiles

Problem 2

On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in miles, \(d\), to the number of hours flying, \(t\), is \(t = \frac{1}{500} d\). How long will it take the airplane to travel 800 miles?

Problem 3

Each table represents a proportional relationship. For each, find the constant of proportionality, and write an equation that represents the relationship.

\(s\) \(P\)
2 8
3 12
5 20
10 40

Constant of proportionality:

Equation: \(P =\)

\(d\) \(C\)
2 6.28
3 9.42
5 15.7
10 31.4

Constant of proportionality:

Equation: \(C =\)

Problem 4

A map of Colorado says that the scale is 1 inch to 20 miles or 1 to 1,267,200. Are these two ways of reporting the scale the same? Explain your reasoning.

(From Unit 1, Lesson 11.)

Problem 5

Here is a polygon on a grid.

A polygon aligned to a square grid.
  1. Draw a scaled copy of the polygon using a scale factor 3. Label the copy A.

  2. Draw a scaled copy of the polygon with a scale factor \(\frac{1}{2}\). Label it B.

  3. Is Polygon A a scaled copy of Polygon B? If so, what is the scale factor that takes B to A?

(From Unit 1, Lesson 3.)