Proportions to Linear Relationships

Which statement is always true?

• A linear relationship is proportional.

• A linear relationship is non-proportional.

• A proportional relationship contains the point (0, 0).

• A non-proportional relationship has a constant rate of change.

A bird-watcher estimates the number of songbirds to the number of birds of prey he will see on a bird-watching trip. His predictions are shown in the graph. What is the rate of change?

A class is taking a trip to the aquarium. The teacher has received only 2 permission slips for every 5 students in the class. Use the graph to determine which line represents the situation.

Kelley is mixing blue and yellow food coloring to make green food coloring for her bakery. The relationship between the amounts of food coloring she mixes can be modeled by the equation \(b = \frac{2}{3}y\) , where b represents the amount of blue food coloring and y represents the amount of yellow food coloring. Which of the following statements are true?

• Kelley uses 2 parts blue for every 3 parts yellow. 

• Kelley uses 3 parts blue for every 2 parts yellow. 

• Kelley uses 2 parts blue for every 5 parts yellow. 

• Kelley uses 5 parts blue for every 2 parts yellow. 

The ratio of boys to girls at a school dance is shown in the graph. Which equation has a greater rate of change than the rate shown on the graph?

Which two statements can you use to conclude that the relationship is non-proportional?

• The graph of the relationship is linear.

• The y-intercept of the graph is (0, 1).

• The relationship has a constant rate of change.

• The equation of the relationship is not in the form y = kx.

Select all characteristics of the graph.

• It is proportional.

• It is linear.

• It is non-proportional.

• It is non-linear.

• The y-intercept is (0, 0).

Which equation represents a proportional relationship?

• y1

• y2

• y3

• y4

• y = x

• y= 4x

• x= 4y

• y= 1/4 x