P2P Session #5: Representing Proportional Relationships

Practice to Practice Session #5

Representing Proportional Relationships

What is a proportion?

• A statement that two rates or ratios are equivalent.

• When determining if two ratios are proportional, think of them as fractions and ask yourself, "are these fractions equivalent?"

Multiple Choice

What number would make this relationship proportional?

 $\frac{10}{20}=\frac{?}{4}$  

• 5

• 2

• 6

• 8

What is a proportional relationship?

• A relationship between two quantities in which the ratio of one quantity to the other is constant.

• A rate of change is a rate that describes how one quantity changes in relation to the other.

• In a proportional relationship, the rate of change is constant.

Relationships are proportional if...

• The rates are CONSTANT!

• If you divide one quantity (y) by the other (x), you will always get the same number.

• This number is called the constant of proportionality (k).

•  $k=\frac{y}{x}$  
  

Examples of Non-Proportional Relationships

• The rates are NOT constant.

• When you divide y by x for each row/column, not all the answers are the same.

• There is NO k!

Multiple Choice

Does this table represent a proportional relationship?

(click on the table to make it bigger!)

• Yes, k = 1/5

• Yes, k = 5

• No there is no k value.

Multiple Choice

What is the constant of proportionality of this proportional relationship? (Click on the table ot make it bigger)

• 4

• 1/4

• 2

• 8

Writing an Equations using the Constant of Proportionality (k)

• Find k in the table by dividing y by x.

• Write an equation for the table (or graph) in the form y = kx.

Multiple Choice

Which equation represents the proportional relationship in the table? (click on the table to make it bigger!)

• y = 17.50x

• y = 4x

• y = 4.35x

• y = 70x

Comparing Proportional Relationships

Which rental car place offers the best deal per day?

Write an equation that represents Rent-All's relationship.

Open Ended

Steven earns extra money babysitting. He charges $31.25 for 5 hours and $50 for 8 hours.

Write an equation to represents the relationship, where y is the amount of money earned in x hours.

Graphs of Proportional Relationships

• Graphs of proportional relationships are straight lines.

• The line starts at the origin (0, 0).

• Sometimes the graphs are written as a set of points (no line drawn through them).

Multiple Choice

Does the following graph represent a proportional relationship?

(Click on the graph to make it bigger)

• Yes

• No

Writing Equations (y = kx) from Graphs

• Look for the point where x = 1. This is the k value!! (unit rate)

• You can use any point (x,y) on the graph and divide y/x.

• Write the equation in the form y = kx.

Another example:

Write the equation of the proportional graph in the form y = kx.

Multiple Choice

Which equation represents the proportional graph?

(Click on the graph to make it bigger) 

•  $y\ =\ \frac{1}{2}x$  

• y = 4x

• y = 2x

•  $y\ =\ \frac{1}{4}x$  

Open Ended

In your own words, explain how you know if a graph displays a proportional relationship?

(Hint - what are the two things you should look for?!)

Open Ended

What is the constant of proportionality, explain how you got your answer.

Use it to write an equation for the proportional relationship.

(Click on the table to make it bigger!)