Understanding Slope and Unit Rates

This lesson covers interpreting the unit rate as slope, focusing on graphing proportional relationships and comparing unit rates using slope. It begins with defining rate and unit rate, explaining their connection to slope. The lesson includes examples of graphing proportional relationships, determining slope, and finding unit rates. Practice problems are provided to reinforce these concepts.

What is a unit rate?

• A comparison of two quantities with the same units

• A rate where the second quantity is one

• A rate expressed as a percentage

• A rate that is always a whole number

How is the slope related to the unit rate in a proportional relationship?

• The slope is half the unit rate

• They are the same value

• The slope is twice the unit rate

• They are always different values

What is the key feature of a graph representing a proportional relationship?

• It passes through the origin

• It is a curved line

• It has a negative slope

• It is a horizontal line

In the waterfall example, what is the slope of the graph?

• 3/1

• 1/3

• 4/3

• 3/4

How do you calculate the unit rate from a slope of 4/3?

• Subtract 3 from 4

• Add 3 to 4

• Multiply by 3

• Divide 4 by 3

In the biking practice problem, what is the unit rate?

• 0.5 miles per minute

• 0.2 miles per minute

• 2 miles per minute

• 5 miles per minute

What is the slope in the biking practice problem?

• 1/5

• 5/1

• 2/10

• 10/2

In the escalator example, what is the slope of the graph?

• 10/6

• 6/10

• 3/5

• 5/3

What is the unit rate in the escalator example?

• 0.5 feet per second

• 0.6 feet per second

• 2.0 feet per second

• 1.5 feet per second

What should you do if your graph and table values differ in the practice problems?

• Recalculate everything

• Ensure they match and are correct

• Ignore the differences

• Use only the graph values