Proportional and Non Proportional Relationships in Tables, Graphs, and Equations

A proportional relationship can be written as an equation in the form ____ = _____  _____

• y = k+x

• y = k-x

• y = kx

• y = k/x

Which of the equations below is proportional?

• y = 6x

• y = 3x + 2

• y = 2x + 4

• y = -2x -1

Proportional tables always have a constant ratio between the values in the table.

• TRUE

• Sometimes

• FALSE

The table shows a proportional relationship. Which of the following is the equation for the number of cookies, c made with each cup of sugar, s

• s = 12c

• s = 24c

• c = 12s

• c = 24s

Answer explanation

Divide the y value in the ratio by the x value to get the constant.

Remember the top row is the x and the bottom row is the y in the ratio.

Proportional equations are written y=kx where k is the constant of proportionality.

Replace the x and y with variables they represent in the ratio.

What is the constant of proportionality?

• $3

• $4

• $2

• $9

A cake recipe calls for 1.5 cups of milk and 3 cups of flour. 

If the cups of milk, x, is compared to the cups of flour, y, what is the equation for y=kx?

• k=2x

• y=0.5x

• k=0.5

• y=2x

Write an equation for the proportional relationship showing number of cups of pineapple juice, p per recipe, r.

Answer explanation

Divide the y value in the ratio by the x value to get the constant.

Remember the left column is the x and the right column is the y in the ratio.

Proportional equations are written y=kx where k is the constant of proportionality.

Replace the x and y with variables they represent in the ratio.

Select all of the graphs that do NOT represent a proportional relationship.

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Answer explanation

Proportional graphs form a straight diagonal line that crosses the origin (0, 0).

If the points are not connected, imagine connecting them and seeing if the graph fits the criteria above.

Select all the tables that show a proportional relationship between x and y in the ratio table.

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Answer explanation

Proportional tables show a consistent constant that each x can be multiplied by to get the corresponding y in the ratio table.

Divide each ratio $\frac{y}{x}$ to see if there is an consistent constant that takes each x to each y in the ratio table.

Select all of the equations that do NOT represent a proportional relationship.

Answer explanation

Proportional equations are written y=kx where k is the constant of proportionality.

The constant can be a whole number, fraction, or decimal.

Other variables can be used to represent the x and y in the equation above.

Proportional equations should show that each x value is multiplied by a constant to get the y value in the ratio.

y = 13x +0 is the same a y = 13x