Direct Variation

A simple relationship between two variables when y changes directly with x (y = kx).

• When x increases, y increases

• When x decreases, y decreases​

​

How it changes is called the Constant of Proportionality (k).

​

​y = 2x

(0,0)

(1,2)

(2,4)

(3,6​

​

​y = 5x

(0,0)

(1,5)

(2,10)

(3,15)​

​

​y = 1/2x

(0,0)

(1,1/2)

(2,1)

(3,1 1/2)​

​

How can we tell if an equation shows direct variation?

• Does the equation fit into y = kx​

• If not, solve for y and check.​

​

​y = 4x y = 3x - 6 3y = 9x y + 2 = x - 6

How can we tell if a table shows direct variation?

• Is the table proportional?

• Can you find the Constant of Proportionality?​

​

How can we tell if a graph shows direct variation?

• Does it form a straigh line?

• Does it pass through the origin?​

​