Linear Relationships and Proportionality

The video tutorial covers Math 8 Unit 3 Lesson 7 on representations of linear relationships. It begins with an activity involving glasses to predict which holds the most water. The lesson progresses to a demonstration using cylinders and marbles to measure volume changes, illustrating how to write equations from real situations. The tutorial explains how to calculate slope, interpret graphs, and understand linear equations, emphasizing the concepts of rate of change and y-intercept. The lesson concludes with practical applications and homework exercises to reinforce learning.

Which glass holds the most water based on the experiment conducted in class?

• Glass B

• Glass A

• All glasses hold the same amount

• Glass C

What was the initial water level in the cylinder before adding any marbles?

• 60 milliliters

• 63 milliliters

• 69 milliliters

• 81 milliliters

How much does the water level rise with each marble added?

• 4 milliliters

• 1 milliliter

• 3 milliliters

• 2 milliliters

What is the slope of the line representing the relationship between marbles and water level?

• 4

• 3

• 2

• 1

In the equation y = mx + b, what does 'b' represent?

• The rate of change

• The y-intercept

• The slope of the line

• The x-intercept

If a linear equation is y = 3x + 12, what is the y-intercept?

• 3

• 12

• 15

• 18

How many months will it take for the bamboo plant to reach 66 inches?

• 12 months

• 24 months

• 18 months

• 15 months

What is the constant proportionality in the first recipe example?

• 2/3

• 4/3

• 3/2

• 1/2

How many cups of flour are needed for 4 cups of sugar in the second recipe?

• 5 cups

• 6 cups

• 8 cups

• 7 cups

What does the constant proportionality represent in a recipe context?

• The total number of ingredients

• The amount of flour needed per cup of sugar

• The ratio of sugar to flour

• The amount of sugar needed