Proportions Relationships

Proportions Relationships

Identify in Equations and Calculate Constant of Proportionality

Proportional relationships in Equations

• Only multiplication and division can be present

• It needs to be in the format y = kx

• k = constant of proportionality

• proportional relationship is also called a direct variation

DIRECT VARIATIONS: y=kx

• y is the dependent variable

• x is the independent variable

• k is the constant of proportionality

Direct Variation Equations:

1) y = -3x

2) y=2x

3) y=x or y=1x

Linear Equations

Although linear equations look like direct variations, they do NOT go through (0,0). This means they are not a proportional relationship

1) y=2x + 3

2) y = 2x - 5

Multiple Choice

Which best describes the equation?
y = 75x

• Proportional
• Nonproportional

Multiple Choice

Which best describes this equation?
y= 3.75x + 2

• Proportional 
• Non-proportional

Multiple Choice

Does the equation show a proportional relationship?

• Yes
• No

Multiple Choice

What is the formula for a proportional relationship?

• y=kx
• y=k/x
• z=ykx
• y=ky

Multiple Choice

Does this equation represent a proportional relationship?

• Yes
• No

Multiple Choice

Does the equation show a proportional relationship?

• Yes
• No

Identifying Constant of Proportionality from an Equations

• y=kx

• k is the constant of proportionality

Multiple Choice

What does k represent in the equation y = kx?

• constant rate of change
• constant of proportionality
• the equation
• x/y

Multiple Choice

The equation y=5x describes a proportional relationship between x and y. What is the constant of proportionality?

• 6

• 4

• 7

• 5

Multiple Choice

In the equation y = 14x, what is the constant of proportionality?

• y
• x
• 14

Multiple Choice

Identify the constant of proportionality.

• k = 1/0.45

• k = 0.45

• k = -0.45

• k = -1/0.45

• none (not proportional)

Multiple Choice

Identify the constant of proportionality.

• k = 2x

• k = 2

• k = 4

• none (not proportional)

Multiple Choice

The constant of proportionality in the equation y = ½x is _______. 

• x
• y
• 1/2
• 2