Understanding Proportional Relationships from Graphs

The video tutorial explores proportional relationships using graphs, focusing on finding the rate of change and writing equations. It explains that proportional graphs pass through the origin and the rate of change is the constant of proportionality, calculated by dividing y by x. The tutorial includes examples such as monarch butterfly migration, baking cookies, movie ticket pricing, and filling a lemonade pitcher, demonstrating how to identify and calculate proportional relationships in each scenario.

What is a key characteristic of a proportional graph?

• It forms a curve.

• It passes through the origin.

• It does not intersect the axes.

• It has a variable rate of change.

How do you calculate the rate of change from a proportional graph?

• Add x and y.

• Divide y by x.

• Multiply x and y.

• Subtract x from y.

In the monarch butterfly example, what is the rate of change?

• 3

• 4

• 5

• 6

What equation represents the relationship in the monarch butterfly example?

• y = 6x

• y = 5x

• y = 4x

• y = 3x

How many chocolate chips are in each cookie according to Maria's example?

• 7

• 8

• 9

• 10

What is the equation for the number of chocolate chips in Maria's cookies?

• y = 7x

• y = 8x

• y = 9x

• y = 10x

What is the rate of change for the movie ticket pricing example?

• 10

• 11

• 13

• 12

What does the point (5, 60) represent in the movie ticket example?

• 5 tickets cost $70

• 5 tickets cost $50

• 5 tickets cost $80

• 5 tickets cost $60

Which graph correctly represents the pitcher being filled with water?

• Graph D

• Graph A

• Graph B

• Graph C

Why is graph D the correct choice for the pitcher example?

• It does not start at the origin.

• It shows 1 cup in 3 seconds.

• It starts filling at 3 seconds.

• It shows 3 cups in 1 second.