M2 T1 L1 - Representations of Proportional Relationships

M2 T1 L1

Representations of Proportional Relationships

Government agencies and civil rights groups monitor enrollment data at universities to ensure that different groups are fully represented. One study focused on the enrollment of women at a certain university. The study found that three out of every five students enrolled were women.

Use the findings of the study to write each ratio.

Multiple Choice

The study found that three out of every five students enrolled were

women.

Write the ratio for:

The number of enrolled female students to the total number of students.

• 3:5

• 3:8

• 2:5

• 2:8

Multiple Choice

The study found that three out of every five students enrolled were

women.

Write the ratio for:

The number of enrolled male students to the total number of students.

• 3:5

• 3:8

• 2:5

• 2:8

Multiple Choice

he study found that three out of every five students enrolled were

women.

Write the ratio for:

The number of enrolled female students to the number of enrolled male students

• 2:5

• 2:8

• 2:3

• 3:2

Multiple Choice

he study found that three out of every five students enrolled were

women.

Write the ratio for:

The number of enrolled male students to the number of enrolled female students

• 3:5

• 3:8

• 2:3

• 3:2

Use the findings of the enrollment study to make predictions

Determine the number of enrolled female students for each given total number of enrolled students. 

15 total students 

 $\frac{3}{5}=\frac{?}{20}$  

5 x 4 = 20   so   we will need to multiply 3 x 4 = 12  the answer is 12. 

Multiple Choice

Use the findings of the enrollment study to make predictions. Three out of every five students enrolled were female.

Determine the number of enrolled female students for each given total number of enrolled students.

35 total students

• 15 females

• 18 females

• 21 females

• 24 females

Multiple Choice

Use the findings of the enrollment study to make predictions. Three out of every five students enrolled were female.

Determine the number of enrolled female students for each given total number of enrolled students. Explain your reasoning.

100 total students

• 55 females

• 60 females

• 45 females

• 40 females

Multiple Choice

Use the findings of the enrollment study to make predictions. Three out of every five students enrolled were female.

Determine the number of enrolled male students for each given total number of enrolled students. Explain your reasoning.

100 total students

• 55 males

• 60 males

• 45 males

• 40 males

Multiple Choice

Use the findings of the enrollment study to make predictions. Three out of every five students enrolled were female.

Determine the number of female students if 800 enrolled students are male.

• 1200 females

• 400 females

• 800 females

• 1000 females

Comparing Ratios and Graphs

The lines y₁ and y₂ each represent a proportional relationship. One line represents the proportional relationship between the number of females enrolled and the total number of students. The other line represents the proportional relationship between the number of males enrolled and the total number of students. 

Multiple Choice

Which line represents females?

• y₁

• y₂

Multiple Choice

Which line represents males?

• y₁

• y₂

Multiple Choice

The ratio of the number of students who enjoy music to the total number of students is slightly more than the ratio of female students to the total number of students.

What would the line comparing students who enjoy music to the total number of students look like on the graph?

• steeper than y₁

  (above the y₁ line)

• in between y₁ and y₂

• less steep than y₂

  (below the y₂ line)

• Not able to graph this line

Proportional Relationships

A proportional relationship is one in which the ratio of the inputs

to the outputs is constant. For example, the ratio of women to men

at a university is 3 : 2. Proportional relationships are always written in

the form y = kx, where x represents an input value, y represents an

output value, and k represents some constant that is not equal to 0.

The constant k is called the constant of proportionality.

Multiple Choice

Identify the constant of proportionality for $y\ =\ \frac{2}{3}x$  

• 2

•  $\frac{2}{3}$  

•  $\frac{3}{2}$  

• 3

Multiple Choice

Identify the constant of proportionality for $y\ =\ \frac{3}{2}x$  

• 2

•  $\frac{2}{3}$  

•  $\frac{3}{2}$  

• 3