Write direct variation equations

Key Notes:

Direct variation can be represented by the equation y = kx.

The variable k is known as the constant of variation, and it cannot equal zero.

Learn with an example

In a direct variation, y = 8 when x =2. Write a direct variation equation that shows the relationship between x and y.

Write your answer as an equation with y first, followed by an equals sign._________

First find the constant of variation. Plug x = 2 and y =8 into the direct variation equation and then solve for k.


y = kx
8 = k(2)
4 = k

Now use k=4 to write the direct variation equation.

y = kx
y = 4x

The direct variation equation is y = 4x.

In a direct variation, y = 16 when x =8. Write a direct variation equation that shows the relation ship between x and y.

Write your answer as an equation with y first, followed by an equals sign._________

First find the constant of variation. Plug x = 8 and y =16 into the direct variation equation and then solve for k.

y = kx
16 = k(8)
2 = k

Now use k=2 to write the direct variation equation.

y = kx
y = 2x

The direct variation equation is y = 2x.

In a direct variation, y = 10 when x =5. Write a direct variation equation that shows the relation ship between x and y.

Write your answer as an equation with y first, followed by an equals sign._________

First find the constant of variation. Plug x = 5 and y =10 into the direct variation equation and then solve for k.

y = kx
10 = k(5)
2 = k

Now use k=2 to write the direct variation equation.

y = kx
y = 2x

The direct variation equation is y = 2x.

let’s practice!