Exploring Constants of Proportionality

Mrs. Piper introduces the concept of graphing proportional relationships, focusing on the constant of proportionality, which is also known as the unit rate or slope. She explains how to calculate it by dividing the y-coordinate by the x-coordinate. Through examples involving a toy car, stars on paper, and miles per hour, she demonstrates how to find the constant of proportionality in different contexts. The lesson emphasizes that the terms constant of proportionality, unit rate, and slope are interchangeable in proportional relationships.

What does the constant of proportionality represent in graphing?

• The intersection point with the y-axis

• The maximum value of y

• The rate at which y increases compared to x

• The curvature of a graph

How do you calculate the slope of a line in a proportional relationship?

• Divide the y-coordinate by the x-coordinate

• Multiply the x-coordinate by the y-coordinate

• Add the x-coordinate to the y-coordinate

• Divide the x-coordinate by the y-coordinate

How is the constant of proportionality related to unit rate?

• Unit rate is always higher

• They are completely unrelated

• They are the same concept

• They are inversely related

What does a straight line through the origin in a graph indicate?

• An undefined relationship

• A non-linear relationship

• A proportional relationship

• A decreasing relationship

In the context of graphing, what is another term for the constant of proportionality?

• Intercept

• Radius

• Slope

• Peak

In the toy car example, what was the constant of proportionality?

• 2 and 2/5

• 5/12

• 2.4

• 12/5

Why can't we use the origin (0,0) to calculate the constant of proportionality?

• Because it gives a value of zero

• Because division by zero is not possible

• Because it results in an undefined value

• Because it always gives a value of one

What does the constant of proportionality indicate in the stars on paper example?

• The number of stars per square inch

• The total number of stars drawn

• The size of each star

• The total area of the paper

What was the unit rate in the example involving speed in miles per hour?

• 50 miles per hour

• 150 miles in 3 hours

• 3 miles in 150 hours

• 1 mile per hour

What is the significance of finding the same constant of proportionality using different points on a graph?

• It verifies the relationship is proportional

• It confirms the graph is non-linear

• It indicates an error in calculation

• It suggests the graph is incomplete