Analyzing Two Variable Relationships

Which list below shows the dependent quantities?

• 0, 1, 2, 3, 4, 5

• 0, 5, 10, 15, 20

• 10, 20, 60, 80, 100

• None of the above

Which situation can be represented by the equation y = 12x?

• A factory uses a total of Y gallons of water at a rate of 12 gallons per hour for X hours.

• A bakery serves a total of Y cakes in one day, in which 12 cakes are served during the first hour and X meals are served during the remaining hours.

• A restaurant prepares a total of Y batches of pizza sauce from 12 pounds of tomatoes, with each batch weighing X pounds.

• A company manufactures a total of 12 plates every hour, with X of the plates made are blue and Y of the plates are green.

Jose travelled at a rate of 0.25 miles per minute. Which equation represents this relationship?

(Remember you can convert a fraction into a decimal, if needed)

• y = ^x/₄

• y = x + 0.25

• y = ​¹⁄₄x

• y = 0.25

What are the independent values?

• adult tickets

• children's tickets

• 0, 10, 20, 30, 40, 50, 60, 70

• 0, 20, 40, 60, 80, 100, 120, 140

How does algebra help in representing relationships between quantities?

• By avoiding equations

• By guessing randomly

• By using only numbers

• By using variables to represent unknown quantities

What do equations in algebra show?

• Relationships between two expressions

• Historical timelines

• Geographical locations

• Biological processes

Why is algebra important in solving mathematical problems?

• It is too complex to be useful

• It helps uncover relationships between numbers and quantities

• It has no practical applications

• It is only used in history

How does algebra help in solving complex problems?

• By providing a systematic way to represent relationships

• By making problems more difficult

• By avoiding unknown quantities

• By using only numbers

Arjun, Abigail, and Luna are having a debate. Arjun says a scatter plot is used to show the distribution of a single variable, Abigail thinks it's to compare the means of two groups, Luna believes it's to display the trend over time. But, who is correct? What is the actual purpose of a scatter plot?

• To show the distribution of a single variable.

• To compare the means of two groups.

• To display the trend over time.

• To display the relationship between two variables.

Zoe, Avery, and Aria are trying to understand the relationship between two variables in a scatter plot. How can they interpret this relationship?

• They can interpret the relationship by observing the pattern or trend of the plotted points.

• They can interpret the relationship by measuring the distance between the plotted points.

• They can interpret the relationship by looking at the color of the plotted points.

• They can interpret the relationship by connecting the plotted points with straight lines.