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
1
10
100
\(a\)

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.)