Understanding Proportional Relationships

What is the constant of proportionality from the table: (x: 2, y: 6), (x: 4, y: 12), (x: 6, y: 18)?

• 3

• 2

• 4

• 5

Write the equation for the proportional relationship represented by the table: (1, 3), (2, 6), (3, 9).

• y = 4x

• y = 3x

• y = 2x

• y = 3x + 1

How can you identify a proportional relationship by graphing?

• A proportional relationship can be identified by a dotted line on a graph.

• A proportional relationship is identified by a straight line through the origin on a graph.

• A proportional relationship is identified by a curved line on a graph.

• A proportional relationship is shown by a line that does not pass through the origin.

Given the graph, how do you find the constant of proportionality?

• k = y + x for any point (x, y) on the line.

• k = x/y for any point (x, y) on the line.

• k = y - x for any point (x, y) on the line.

• k = y/x for any point (x, y) on the line.

Write the equation for the proportional relationship shown in the graph with points (0,0), (2,4), (4,8).

• y = x

• y = 2x

• y = 2x + 1

• y = 4x

How can you identify proportional relationships from both graphs and equations?

• Proportional relationships can be identified by straight lines through the origin in graphs and equations of the form y = kx.

• Proportional relationships are represented by curves in graphs and equations of the form y = k + x.

• Proportional relationships can be identified by horizontal lines in graphs and equations of the form y = k.

• Proportional relationships are shown by lines that do not pass through the origin in graphs and equations of the form y = mx + b.

From the table (x: 1, y: 2), (x: 2, y: 4), (x: 3, y: 6), is this a proportional relationship?

• This relationship is quadratic, not proportional.

• Yes, this is a proportional relationship.

• No, this is not a proportional relationship.

• The relationship is only proportional for x = 1 and x = 2.

Complete the table and graph the proportional relationship: (x: 1, y: 5), (x: 2, y: 10).

• (x: 1, y: 10), (x: 2, y: 15)

• (x: 3, y: 10), (x: 4, y: 25)

• The completed table is: (x: 1, y: 5), (x: 2, y: 10), (x: 3, y: 15), (x: 4, y: 20).

• (x: 1, y: 6), (x: 2, y: 12)

Create a graph for the word problem: A car travels 60 miles in 1 hour. How far will it travel in 3 hours?

• 180 miles

• 300 miles

• 240 miles

• 120 miles

Interpret the graph of the proportional relationship between hours worked and money earned.

• The relationship is non-linear, with money earned fluctuating unpredictably with hours worked.

• The relationship is exponential, with money earned decreasing as hours worked increase.

• The relationship is linear and proportional, with money earned directly increasing with hours worked.

• The graph shows a constant relationship, where money earned remains the same regardless of hours worked.