Identifying Proportional Relationships and Slope

The video tutorial explores the concepts of unit rate and slope, highlighting their similarities as expressions of rate of change. It explains unit rate as a measure per one unit, using examples like miles per gallon, and describes slope as a whole number or a ratio in lowest terms. The tutorial demonstrates how to find slope and unit rate using different representations: graphs, equations, and tables. Through these examples, viewers learn to calculate and interpret these mathematical concepts effectively.

What do unit rate and slope have in common?

• Both are calculated using addition.

• Both are expressions of rate of change.

• Both are always whole numbers.

• Both are used to measure distance.

What is the main difference between unit rate and slope?

• Unit rate is always a whole number.

• Slope is always a fraction.

• Slope is always greater than unit rate.

• Unit rate is per one unit, while slope can be a whole number or a ratio.

What is the relationship between unit rate and slope in a proportional relationship?

• They are always equal

• Unit rate is the inverse of slope

• Unit rate is the slope for one unit

• Slope is always greater than unit rate

Which of the following is an example of a unit rate?

• Gallons per mile

• Miles per gallon

• Miles per hour

• Hours per mile

How is slope usually expressed?

• As a fraction with a denominator of 10

• As a percentage

• As a whole number or a ratio in lowest terms

• As a decimal

Which of the following is NOT a way to represent slope?

• As a whole number

• As a ratio in lowest terms

• As a decimal

• As a percentage

What kind of line represents a proportional relationship on a graph?

• A straight line through the origin

• A vertical line

• A curved line

• A horizontal line

How can you identify a proportional relationship on a graph?

• By looking for a curved line

• By finding a straight line through the origin

• By locating a vertical line

• By identifying a horizontal line

In the dog walking example, what is the unit rate?

• $4 per hour

• $6 per hour

• $3 per hour

• $5 per hour

What does the point (1, 4) represent in the dog walking example?

• The slope of the line

• The unit rate of $4 per hour

• The total earnings

• The number of dogs walked