Graphs of Proportional Relationships and Constant of Proportionality

This video tutorial covers the concept of proportional relationships, focusing on how to determine if a table or graph represents such a relationship. It explains the constant of proportionality, denoted as 'k', and how to calculate it from tables and graphs. The video also discusses the characteristics of graphs that indicate proportional relationships, such as passing through the origin. The lesson includes practical examples and exercises for identifying and calculating the constant of proportionality.

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

• The sum of all values in the first column equals the sum in the second column.

• There is a constant value that, when multiplied by the first column, gives the second column.

• The product of values in the first column is always greater than in the second column.

• The values in the first column are all even numbers.

Which of the following is NOT a method to identify a proportional relationship in a table?

• Calculating the constant of proportionality as a ratio of y to x.

• Verifying that the sum of the first column equals the sum of the second column.

• Ensuring each value in the first column is multiplied by a constant to get the second column.

• Checking if the cross-products of rows are equal.

How can you determine the constant of proportionality from a table?

• By dividing any value in the second column by the corresponding value in the first column.

• By adding all the values in the table.

• By multiplying all values in the first column by 2.

• By subtracting the smallest value from the largest value in the table.

What does the constant of proportionality represent in a proportional relationship?

• The difference between the largest and smallest values.

• The sum of all values in the table.

• The ratio of y to x in a proportional relationship.

• The product of all values in the second column.

What is a necessary condition for a graph to represent a proportional relationship?

• The line must have a positive slope.

• The line must pass through the origin.

• The line must be vertical.

• The line must be horizontal.

If a line on a graph passes through the origin, what does it indicate?

• The graph represents a proportional relationship.

• The graph has no relationship.

• The graph represents a non-linear relationship.

• The graph represents a quadratic relationship.

How can you find the constant of proportionality from a graph?

• By finding the slope of the line.

• By identifying any point on the line and calculating the ratio y to x.

• By measuring the length of the line.

• By counting the number of points on the line.

What is the constant of proportionality if the ordered pair on a line is (2, 4)?

• 3

• 2

• 1

• 4

What is the constant of proportionality if the ordered pair on a line is (5, 2)?

• 1/2

• 2/5

• 5/2

• 2

What is the significance of the constant of proportionality in a proportional relationship?

• It determines the slope of the line.

• It indicates the strength of the relationship.

• It is the ratio that remains constant for all pairs of values.

• It shows the difference between x and y values.