Constant of Proportionality Concepts

This lesson, led by Mr. Weaver, covers proportional relationships and equations. Students learn to write equations in the form y = kx to represent proportional relationships and identify the constant of proportionality from tables or stories. Examples include coffee brewing, lemonade mixing, and paint mixing, illustrating how to calculate and apply constants of proportionality. The lesson emphasizes understanding the relationship between inputs and outputs in tables and how to express these relationships as equations.

What is the format of an equation that represents a proportional relationship?

• y = k + x

• y = kx

• y = x/k

• y = mx + b

In the coffee brewing example, what is the constant of proportionality if 4 cups of coffee require 2 tablespoons of grounds?

• 4

• 1/4

• 2

• 1/2

How do you calculate the constant of proportionality in a table?

• Add the start and end

• Subtract the start from the end

• Divide the end by the start

• Multiply the start by the end

In the lemonade mix example, what is the constant of proportionality when 3 parts of water require 1/4 parts of mix?

• 3/4

• 12

• 1/12

• 4/3

What operation is used to find the reciprocal constant of proportionality?

• Multiplication

• Subtraction

• Division

• Addition

What is the reciprocal of a constant of proportionality of 12?

• 1/6

• 12

• 1/12

• 6

What does the 'k' represent in the equation y = kx?

• The y-intercept

• The constant of proportionality

• The x-intercept

• The slope

In the paint mixing example, if 4 parts of red paint are needed for blue paint, what is the constant of proportionality?

• 2

• 1

• 4

• 1/4

How can you express the relationship between red and blue paint in an equation?

• b = r/4

• r = 4b

• b = 4r

• r = b/4

If you know the amount of blue paint needed, how do you find the amount of red paint?

• Multiply by 1/4

• Add 4

• Divide by 4

• Multiply by 4