Constant of Proportionality

Constant of Proportionality

Ask yourself...

What multiplication will get me from x to y?

If I start with x and end with y, what did I multiply x by?

Does it look like I need to divide to get from x to y? If so, what would that look like as multiplication?

What if I work backwards and compare the y values to the x values?

Constant of Proportionality

The ratio between quantities that proves that x is directly proportional to y. The constant of proportionality, often identified as k , is the number that constantly multiplies with x to get y.

This is shown by the formula y=kx

k can be found by comparing the y values to the x values (in that order) which is shown by the formula k=y/x

The constant of proportionality can include any rational numbers including whole numbers, decimals, fractions, and negatives.

Multiple Choice

To find the constant (k), we would ask ____ times what number is ____?

• x times what number is y?

• y times what number is x?

Multiple Choice

To find the constant (k), we can work backwards and create ratios that compare the values in the order _____ to ______.

• x to y

• y to x

• k to x

• y to k

Multiple Select

Select the TWO equations that find the constant of proportionality.

• y/x = k

• k =x/y

• x = k/y

• y = kx

Multiple Choice

Which equation is used to represent the constant of proportionality?

• x = ky

• y = x

• y = kx

Multiple Choice

In the equation y = 14x, what is the constant of proportionality?

• y

• x

• 14

• 14x

Multiple Choice

Which equation helps you work backwards to solve for k, the constant of proportionality?

• k = x/y

• k = y/x

• k = y + x

• k = 2x

y = kx

The formula states that any x value multiplied by a number, k, will result in the y value. If the relationship between x and y is proportional, it will not require any steps other than multiplication.

k is the constant of proportionality when comparing ratios x : y

x is the first term in a ratio, the independent variable, the input

y is the second term in a ratio, the dependent variable, the output

If the formula says y = 5x, then the constant of proportionality is 5. This means that in the table if you multiply all the x values by 5, you will get the y values.

Multiple Choice

Identify the constant of proportionality in the equation.

• k = 2x

• k = 2

• k = 4

• none (not proportional)

Multiple Choice

Which equation is NOT a proportional relationship?

• y = 2x - 3

• y = 150x

• y = 5/4x

Multiple Choice

The constant of proportionality in the equation y = ½x is _______. 

• x
• y
• 1/2
• 2

Multiple Select

Select ALL equations that are proportional.

• y = 3x

• y = 25x + 8

• y = 7x

• y = 2x - 1

• y = 4000x

k = y/x

The equation that helps us work backwards to the constant of proportionality.

This is the equation that states that the constant of proportionality can be found by comparing the y values to the x values in that order.

When you create ratios in the format y : x and they all simplify to the same ratio, then that number is the constant of proportionality.

Once you have a number that you have identified as "k" then you should test it on the x values. Multiply all the x values by k and see if the product is the corresponding y values.

Multiple Choice

Is the given table a proportional relationship? If so, what is the constant?

• Yes; 1/3

• Yes; 3

• Yes; 5

• No

Multiple Choice

The table is proportional, what is the constant of proportionality?

• 4

• 2

• 1/4

• -4

Multiple Choice

The table is proportional, what is the constant of proportionality?

• 7

• 3.3

• 3/10

• 14

Multiple Choice

Which of the tables above has a constant of proportionality of $0.20?

• A & C

• A

• B

• All of them

Multiple Choice

Determine the constant of proportionality for the table. Express your answer as y = kx

• y = 30k

• y = 30x

• y = 0.03x

• y = 9x

Multiple Choice

Determine the constant of proportionality for the table. Express your answer as y = kx

• y = 1/2x

• x = 1/2y

• y = 2x

• k = x

Multiple Choice

Using the data from the table, which equation represents the relationship between x and y values?

• y = 33 + x

• y = 24 + x

• y = 12x

• y = -12x

Multiple Choice

Write the equation for the table given.

• y = 16x
• y=8x
• y=12x

Multiple Choice

Write an equation for this relationship.

• y=18x
• y=18.50x
• y=22.50x
• y=22x