Proportional Relationships and Functions

This video tutorial by Mr. Math Blog covers lesson 3.1 on representing proportional relationships for eighth-grade students. It explains how proportional relationships graph as lines through the origin, using tables, equations, and graphs to represent them. The tutorial includes real-world examples, such as calculating distances in leagues and miles, and earnings based on hours worked. It also discusses the constant of proportionality and how to derive equations from proportional relationships.

What is a key characteristic of proportional relationships when graphed?

• They form a parabola.

• They have a vertical line.

• They pass through the origin.

• They form a curve.

In the historical example, how many miles does one league represent?

• Three miles

• Four miles

• Two miles

• One mile

What is the constant of proportionality in the table example?

• 3/1

• 2/1

• 1/3

• 1/2

How is the constant of proportionality represented in the equation y = kx?

• As y

• As xy

• As x

• As k

If Megan earns $12 per hour, what is the equation representing her earnings?

• y = 12x

• y = x + 12

• y = 12 + x

• y = x/12

In the quarters and cents example, what does x represent?

• Amount in dollars

• Amount in dimes

• Amount in nickels

• Amount in quarters

How many bicycles are produced per hour at Speedy Bike Works?

• 20

• 25

• 10

• 15

What does the graph of a proportional relationship always pass through?

• The point (1,1)

• The origin

• The y-axis

• The x-axis