Proportional and Nonproportional Relationships

In this lesson, Miss Go teaches students how to identify proportional and nonproportional relationships in graphs. Students learn to determine if two quantities are proportional by graphing them on a coordinate plane and checking if the graph is a straight line through the origin. The lesson includes examples of both proportional and nonproportional relationships, with a focus on analyzing tables and plotting points on graphs. Key characteristics of proportional graphs, such as lying on a straight line and passing through the origin, are emphasized.

What is the main focus of today's lesson?

• Learning about quadratic equations

• Understanding the Pythagorean theorem

• Exploring geometric shapes

• Identifying proportional and nonproportional relationships in graphs

How can you determine if two quantities are proportional using a table?

• By adding the input and output values

• By dividing the output by the input to find a constant ratio

• By subtracting the input from the output

• By multiplying the input and output values

What is the constant of proportionality in the given example with candy bars?

• 2.0

• 0.5

• 1.5

• 3.0

What are the two main characteristics of a proportional graph?

• The graph is a curve and does not pass through the origin

• The graph is a curve and starts at the origin

• The graph is a straight line and passes through the origin

• The graph is a straight line and does not pass through the origin

In the second example, why is the relationship not proportional?

• The points form a curve and start at the origin

• The points form a straight line but do not start at the origin

• The points do not form a straight line and do not start at the origin

• The points form a straight line but one point does not lie on it

What does it mean if a graph starts at the origin but the points do not form a line?

• The relationship is quadratic

• The relationship is nonproportional

• The relationship is proportional

• The relationship is linear

In the final example, why is the relationship considered nonproportional?

• The line is straight but does not pass through the origin

• The line is curved and passes through the origin

• The line is straight and passes through the origin

• The line is curved and does not pass through the origin

What is a key indicator that a graph represents a proportional relationship?

• The graph is a straight line that passes through the origin

• The graph is a straight line that does not pass through the origin

• The graph is a curve that passes through the origin

• The graph is a curve

What does the shorthand symbol of three dots in a triangle represent?

• However

• Therefore

• Because

• Moreover

What is the outcome when two proportional quantities are graphed?

• The points form a curve

• The points form a straight line that passes through the origin

• The points form a scattered plot

• The points form a straight line that does not pass through the origin