Proportional Relationships and Graphs

In this lesson, Kirk Weiler explores proportional relationships, focusing on the concept that two variables are proportional if their ratio is constant. The lesson includes exercises on corn plant growth and gasoline cost, demonstrating how to calculate ratios, unit rates, and graph proportional relationships. Key takeaways include understanding that proportional relationships form straight lines through the origin on a graph and recognizing the unit rate as a critical component of these relationships.

What is the main focus of the lesson on proportional relationships?

• Understanding constant ratios between variables

• Studying historical events

• Learning about quadratic equations

• Exploring geometric shapes

In the corn plant problem, what is the ratio of height to days in simplest form?

• 5:2

• 3:1

• 2:5

• 6:15

How is the unit rate of the corn plant's growth expressed?

• 5 inches per day

• 2.5 inches per day

• 1.5 inches per day

• 3 inches per day

What pattern is observed when graphing the corn plant's growth data?

• The points form a straight line

• The points form a circle

• The points form a curve

• The points are scattered randomly

What are the two key features of a proportional relationship graph?

• Passes through the origin and forms a straight line

• Forms a curve and passes through the origin

• Forms a straight line and passes through the y-axis

• Passes through the x-axis and forms a curve

In the gas station graph exercise, what is the constant of proportionality?

• $3.25 per gallon

• $3.75 per gallon

• $4.00 per gallon

• $2.50 per gallon

How much would a customer pay for 11 gallons of gasoline at $3.25 per gallon?

• $35.75

• $30.00

• $40.00

• $32.50

If Jenna has $60, will she have enough to fill a 20-gallon tank at $3.25 per gallon?

• No, she needs $65

• Yes, she has enough

• No, she needs $70

• Yes, she will have $5 left

What is a key takeaway about proportional graphs?

• They are always horizontal

• They always pass through the origin

• They never pass through the origin

• They form a curve