Understanding Proportional Relationships

Lesson 14 focuses on understanding the constant of proportionality through different representations: graphs, equations, and tables. It explains how to identify and calculate the constant of proportionality, emphasizing the unit rate and scale factor. The lesson also distinguishes between proportional and non-proportional relationships, highlighting the characteristics of each in various representations.

What are the three representations discussed in the lesson?

• Table, Chart, and Diagram

• Equation, Diagram, and Chart

• Graph, Table, and Equation

• Graph, Table, and Diagram

In a graph representing a proportional relationship, what is the significance of the line passing through the origin?

• It means the x-intercept is non-zero.

• It shows that the y-intercept is zero.

• It suggests the graph is not proportional.

• It indicates a non-linear relationship.

How is the constant of proportionality determined from a graph?

• By multiplying the x and y coordinates.

• By subtracting the x-coordinate from the y-coordinate.

• By adding the x and y coordinates.

• By dividing the y-coordinate by the x-coordinate.

What does the equation y = 7/4x represent in terms of proportionality?

• y is 7/4 times more than x.

• y is unrelated to x.

• y is 7/4 times less than x.

• y is equal to x.

In the equation representation, what does 7/4 signify?

• The slope of the line.

• The constant of proportionality.

• The x-intercept.

• The y-intercept.

How is the constant of proportionality verified in a table?

• By checking if x divided by y is constant.

• By ensuring all x-values are equal.

• By checking if y divided by x is constant.

• By ensuring all y-values are equal.

What happens to the constant of proportionality when you divide 21 fourths by 3?

• It becomes 7 fourths.

• It becomes 1 fourth.

• It becomes 21 fourths.

• It becomes 3 fourths.

What indicates a non-proportional relationship in a graph?

• The line is straight and has a negative slope.

• The line is straight and has a positive slope.

• The line is straight and passes through the origin.

• The line is curved or does not pass through the origin.

Which of the following is NOT a characteristic of a proportional relationship?

• The table shows a constant ratio of y to x.

• The equation can be expressed as y = kx.

• The graph is a straight line through the origin.

• The graph is a curved line.

If a table does not show a constant ratio of y to x, what does it indicate?

• The table is incorrect.

• The values of x and y are equal.

• The relationship is proportional.

• The relationship is non-proportional.