Understanding Proportional Relationships and Unit Rates

This lesson focuses on interpreting the unit rate as the slope of a graph. It begins by defining the unit rate and its relationship to slope, emphasizing that in proportional relationships, the unit rate and slope are identical. The lesson includes examples of graphing proportional relationships using unit rates, and methods to calculate slope and unit rate from graphs and tables. Students are given practice problems to reinforce these concepts, with solutions provided for self-assessment.

What is the primary goal of the lesson on interpreting unit rate as slope?

• To solve complex algebraic equations

• To compare different types of rates

• To graph proportional relationships using unit rate

• To understand the concept of unit rate

How is a rate defined in the context of this lesson?

• A comparison of two quantities with the same units

• A comparison of two quantities with different units

• A measure of speed

• A type of graph

What is a unit rate?

• A rate expressed as a percentage

• A rate where the second quantity is one

• A rate where the first quantity is one

• A rate that is always a whole number

In a proportional relationship, what is true about the graph?

• It always passes through the point (1,1)

• It always passes through the origin (0,0)

• It is always a horizontal line

• It is always a vertical line

What is the first step in using the unit rate to graph proportional relationships?

• Find the y-intercept

• Calculate the slope

• Set up a table of values

• Draw the axes

In the waterfall example, what is the unit rate of water flow?

• 3 cubic feet per second

• 4 cubic feet per second

• 1.3 cubic feet per second

• 1 cubic foot per second

How do you find the slope from a graph?

• By dividing the change in y by the change in x

• By subtracting the x values from the y values

• By adding the x and y values

• By measuring the distance between two points

In the practice problem, what is Thomas's unit rate of biking?

• 0.1 miles per minute

• 0.2 miles per minute

• 1 mile per minute

• 0.5 miles per minute

What is the slope of the escalator in the third example?

• 2/3

• 1/2

• 5/3

• 3/5