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.
Problem 5
Here is a polygon on a grid.

Draw a scaled copy of the polygon using a scale factor 3. Label the copy A.

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

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