Transformations, Functions, and Proportionality

This video tutorial covers various mathematical concepts for eighth-grade students. It begins with an introduction to linear relationships using recipes for banana cakes, explaining how to calculate the amount of flour needed for a given amount of sugar. The video then discusses the constant of proportionality in these recipes. It moves on to geometry, showing how to identify transformations that demonstrate figure similarity. The tutorial also includes graphing linear equations with different slopes and y-intercepts. Finally, it presents a problem involving the growth of a bamboo plant, teaching how to write and solve equations to predict its height over time.

In the first banana cake recipe, how many cups of flour are needed for 4 cups of sugar?

• 7 cups

• 4 cups

• 5 cups

• 6 cups

What is the constant of proportionality in the second banana cake recipe?

• 1

• 1.5

• 1.75

• 2

Which transformation is NOT used to show similarity between two figures?

• Translation

• Reflection

• Rotation

• Scaling

What is the slope of the line with the equation y = 1/5x + 1?

• 1/2

• 1/3

• 1

• 1/5

For the line y = 3/5x + 3, what is the y-intercept?

• 2

• 3

• 1

• 4

What is the slope of the line y = 6/5x + 2?

• 5/6

• 2

• 6/5

• 1

What is the y-intercept of the line y = 6/5x + 2?

• 0

• 1

• 2

• 3

What is the equation that describes the height of the bamboo plant over time?

• h = 3t + 12

• h = 2t + 12

• h = 3t + 10

• h = 2t + 10

After how many months will the bamboo plant be 66 inches tall?

• 20 months

• 18 months

• 15 months

• 12 months

What is the slope of the equation h = 3t + 12?

• 4

• 3

• 1

• 2