Exploring Proportional Relationships in Grade 8

This video introduces linear relationships, focusing on representing proportional relationships through graphing. It uses examples like water tanks and a stew recipe to illustrate the importance of choosing appropriate scales and representations. The video also compares different proportional relationships, such as earnings, to highlight the concept of rate of change.

What is the purpose of graphing in understanding relationships?

• To help make sense of relationships

• To replace numerical analysis

• To make the relationships look complex

• To confuse the data

At what rate is tank A being filled?

• 110 liters per minute

• 50 liters per minute

• 2.75 liters per minute

• 2.2 liters per minute

Why is it important to choose a helpful scale for graph axes?

• To confuse the readers

• To use more ink when printing

• To accurately answer questions posed by the situation

• To make the graph look fuller

How many carrots are needed if 150 potatoes are used in the recipe?

• 300 carrots

• 75 carrots

• 150 carrots

• 225 carrots

What does the constant of proportionality represent in an equation?

• The number we multiply by the variable

• The slope of the graph

• The number we divide by the variable

• The number added to the variable

What is the slope of the graph in a proportional relationship?

• The product of x and y values

• The difference in y-values

• The sum of x-values

• The constant of proportionality

What is the rate of change in a proportional relationship?

• The total amount of output

• The amount the output changes when the input increases by 1

• The amount the input changes when the output increases by 1

• The total amount of input

How do we find Jada's rate of change?

• By adding her earnings to the time worked

• By multiplying the time worked by her earnings

• By dividing her earnings by the time worked

• By subtracting her earnings from the time worked

Who earns a higher rate per hour?

• Jada

• Both earn the same

• It cannot be determined

• Clare

How much more does Clare earn than Jada after 20 hours of work?

• $25

• $20

• $15

• $30