Proportional Relationships, Tables and Equations

Is this graph proportional?

• Yes

• No

Is the graph proportional or non proportional?

• proportional

• non proportional

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

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• 
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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

Write an equation for this relationship.

Remember: y = kx

• y = 4x

• y = (1/8)x

• y = (1/4)x

• y = 8x

What is the equation for this table?

• y=0.125x

• y=8x

• y=2x

• y=5x