Proportionality

Proportionality Test Study Guide

Make sure to take notes in your notebooks.

​Your test will cover

​1) Identifying if a relationship is proportional

​2) Finding the constant of proportionality

​3) Review of previous material (including circles, conversions,

​Identifying if a Relationship is Proportional

​To determine if a relationship is proportional, you must determine which representation you're looking at.

​

A graph is proportional if it is LINEAR and PASSES THROUGH THE ORIGIN.

​

​Tables are proportional if they show a CONSTANT RATIO of y divided x.

​

​Equations are proportional when they are MULTIPLICATIVE.

​

​Ratios are proportional if they are equivalent or if their cross products are the same.

Multiple Choice

Is the graph proportional or not?

• proportional

• NOT proportional

Multiple Choice

Is the table proportional or not?

• proportional

• NOT proportional

Multiple Choice

Is the equation proportional or not? $$y=0.5x+5$$

• proportional

• NOT proportional

Multiple Choice

Is the graph proportional or not?

• proportional

• NOT proportional

Multiple Choice

Is the equation proportional or not? $$y=2x-10$$

• proportional

• NOT proportional

Multiple Choice

Is the table proportional or not?

• proportional

• NOT proportional

Multiple Choice

Is the graph proportional or not?

• proportional

• NOT proportional

Multiple Choice

Is the equation proportional or not? $$y=\frac{7}{8}x$$

• proportional

• NOT proportional

Multiple Choice

Is the table proportional or not?

• proportional

• NOT proportional

Multiple Choice

Is the equation proportional or not? $$y=-3x$$  

• proportional

• NOT proportional

​Constant of Proportionality

​The constant of proportionality is represented by the variable k.

​It is the number that is multiplied by x in the equation y=kx.

​

​Sometimes, the constant of proportionality is also called the rate of change or the unit rate.

​

​To solve for the constant of proportionality, we divide y divided by x.

Multiple Choice

Which of the following is the correct formula for finding the constant of proportionality?

• k = x/y
• k = y/x
• y = k/x
• x = k/y

​Constant of Proportionality from Graphs

​To find the constant of proportionality from a graph, choose an ordered pair on the line and divide y divided by x.

​

​Remember, ordered pairs are written as (x,y).

​

Multiple Choice

Which of the following ordered pairs is NOT part of the graph above?

• (2, 94)
• (4, 188)
• (282, 6)
• (8, 376)

Multiple Choice

What is the constant of proportionality for the following graph?

• 80
• 20
• 40
• 160

Multiple Choice

What is the ordered pair that represents the unit rate?

• (1, 15)

• (15, 1)

• (4, 60)

Multiple Choice

Identify the constant of proportionality.

• k = 6

• k = 12

• k = 1/6

• k = 1/12

• none (not proportional)

​Tables

​You can also find the constant of proportionality from tables.

​

​Choose 1 row from the table and divide y divided by x.

Multiple Choice

What is the constant of proportionality?

• 3
• 4
• 2
• 5

Multiple Choice

Which of the tables above has a constant of proportionality of $0.20?

• A & B
• A
• B
• All of them

Multiple Choice

What is the constant of proportionality for the table above?

• 2
• 1/2
• 3
• None of the above

Multiple Choice

What is the constant of proportionality of the relationship represented by the table above?

• 75
• 0.013
• 1/75
• None of the above

Multiple Choice

The point (0, 0) is called the origin.

• True
• False

Multiple Choice

The horizontal axis is the y-axis.

• True
• False

Multiple Choice

According to the graph above, 5 bags of luggage weighs 150 pounds.

• True
• False

​Constant of Proportionality from Equations

​The constant of proportionality is the number multiplied times the x.

​

​

In the equation y=4x, the constant of proportionality is 4.

​There are also some other important questions on this test. These will include:

​

CIRCLES

​CONVERSIONS

​FRACTIONS

​DECIMALS

Multiple Choice

What number is pi?

• 1.41

• 2.00

• 3.14

• 5.14

Multiple Choice

What is the "formal" definition of pi?

• 22/7
• 3.1415926
• the ratio of a circle's circumference to its diameter
• the surface area of a sphere of diameter 22/7

Multiple Choice

The equation C = πd, is used to find the circumference of a circle given it's diameter. This formula can be rearranged to solve for pi. Which equation is written correctly to solve for pi?

• π = Cd

• π = C ÷ d

• π = d ÷ c

• π = C - d