Algebra 1

Lesson 3-6



Real-World Example 1 Proportional Relationships

GEOMETRY The table below shows the radii of circles and their circumference.



Radius 1 2 3 4 5

Circumference 2 4 6 8 10



a. Graph the data. What conclusion can you make

about the relationship between the radius of a

circle and the circumference?

The graph shows a linear relationship between the

radius r of the circle and the circumference C. The

graph also passes through the point (0, 0) because

when the radius of a circle is 0, the circumference is 0.

Therefore, the relationship is proportional.



b. Write an equation to describe this relationship.

Look at the relationship between the domain and range to find a pattern that can be described

by an equation.

+1 +1 +1 +1



Radius 1 2 3 4 5

Circumference 2 4 6 8 10



+2 +2 +2 +2



The difference between the values for the radius r is 1. The difference in the values for the

2

circumference C is 2. This suggests that the k-value is or 2. So, the equation is C = 2r.

1

You can check this equation by substituting values for r into the equation.



CHECK If r = 1, then C = 2(1) or 2. 

If r = 2, then C = 2(2) or 4. 

If r = 3, then C = 2(3) or 6. 



c. Use this equation to predict the circumference of a circle that has a radius of 11 units.

C = 2r Original equation

= 2(11) r = 11

= 22 Multiply.



A circle that has a radius of 11 units has a circumference of 22 units.

Example 2 Nonproportional Relationships

Write an equation in function notation for the graph.

Understand You are asked to write an equation of the relation that is

graphed in function notation.



Plan Find the difference between the x-values and the

difference between the y-values.



Solve Select points from the graph and place them in a table.

+1 +1 +1 +1



x 0 1 2 3 4

y -1 -4 -7 -10 -13



-3 -3 -3 -3



The difference between the x-values is 1, and the difference between the y-values is -3.

This suggest that y = -3x.



If x = 1, then y = -3(1) or -3. But the y-value for x = 1 is -4. This is a difference of -1.

Try some other values in the domain to see if there is a pattern.



x 0 1 2 3 4

-3x 0 -3 -6 -9 -12

y -1 -4 -7 -10 -13 y is always 1 less than -3x.



This pattern shows that -1 should be added to one side of the equation. Thus, the

equation is y = –3x – 1.



Check Compare the ordered pairs from the table to the graph. The points correspond. 