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direct variation is when two variables have a relationship in which one varies directly to the other. As one variable increases the other increases, as one decreases the other variable decreases. 

  • The number of points scored by a soccer team is in direct proportion to the number of goals made.
  • The profit of a movie is in direct proportion to the number of tickets sold.
  • If you earn an hourly wage, the amount of money you earn is in direct proportion to the number of hours you work.
  • The amount of time it takes to drive across the country is in direct proportion to the speed traveled.

Video Tutorial: Direct Variation/Proportion Word Problem

Video Tutorial: Direct Variation Word Problem

Real life examples of direct variations

You also can use T-tables in order to determine if the variation is direct and to find K, your constant of variation.

Direct Variation -7th Grade Math

t-tables for graphing
In this example  as x increases y also increases 

y increases by the factor of 3 each time

  • Multiply x by 3, so k = 3. 
  • Plug 3 into the formula  y = kx
  • This can be written y= 3x
graph showing direct variation
  • A direct variation is a linear equation, and as the value of x increases so does the value of y
  • A direct variation is expressed in the form y=kx with the slope defined by k which is your constant of variation.

What does the K stand for in direct variation?

The k in the direct variation formula is called the constant of variation. It tells you how much y will change as x changes. For instance, look at y = 2x  k=2 therefore, as x changes y will change 2 times this value.
if x=2 y=4, if x=3, y=6

Here is another way to think about the constant of variation. If you play on a soccer team your score will vary in each game depending on the number of goals made. The score, and the number of goals scored can vary in the equation, but the number of points you get for a goal will remain constant. The points for goals scored will be your constant of variation. No matter what the score is, when you divide this by goals scored, you will always get the number of points you get per goal. ( Each goal count as one)

Direct Variation Problems

Given the ordered pair ( 3,9) write an equation of the direct variation.

Step 1. Plug in your given information in the direct variation formula                       y=kx
         9= k+3

Step 2. Divide both sides by 3    9/3 = K

Step 3. K=3

Step 4. Now plug 3 into the formula y=kx  
              y =-3x

Direct Variation Word Problems

Word Problem # 1 The Ford F150 can travel 150 miles on 10 gallons of gas. How much gas is required to travel 750 miles? 
Word Problem # 2 Drew gets paid hourly at his job. If Drew gets $50 dollars for a 5 hour shift,how much will he be paid for a 7 hour shift? Find K and write an equation to solve this question.

Direct variation or Inverse variation?

The video goes over each equation, and classifies it as direct or inverse variation.
Direct variation equations are written  y = kx
Inverse variations are written y = k/x

m= 5p

C = P/-4

R = 9t

y = w/18

Answer to word problem #1
Answer to word problem #2
The linear equation graph at the right shows that as the x value increases, so does the y value. This is an example of a direct variation
Direct Variation Graph
Common Core Standard  7.RP.A.2a 7th Grade Math
Keywords:  7th Grade Math, Proportional relationship, Common Multipliers