Variation

Variation

1. direct

   • equation: y=kx
   • If X goes up Y will go up and if X goes down Y will go down
     • This graph shows direct variation
       • You can tell it's direct variation because you can see X goes up as Y goes up and the y-intercept is 0
   • the y-intercept is always 0

2. inverse

   • equation: y=k/x
   • If X goes up, Y will go down and if X goes down, Y will go up
     • This graph shows inverse variation
       • You can tell it's inverse because you can see as Y increases X decreases

3. How to tell if a chart is direct, inverse, or neither

   • This chart shows direct variation
     • You can tell it's direct variation because you can see Y goes up as X goes up
       • You can also see that the Y-intercept will be 0
   • This chart shows inverse variation
     • You can tell it's inverse variation because you can see X goes down as Y goes up
   • This chart shows neither direct or inverse variation
     • You know it is not direct because Y does not go up and X does not go down or Y does not go down and X does not go up
       • You know it is not inverse because on variable does not go up as the other goes down

4. Word Problems

   • inverse
     • The more minutes a basketball player player plays results in them making less shots for the rest of the game. If a player played for 10 minutes
       • and made 6 shots for the rest of the game, how many shots would they make for the rest of the game if they played for 30 minutes?
       • first you set up the equation to solve for K. You would plug in 10 for X and 6 for Y
         • 6=K/10
           • times both sides by 10 then you get 60 for K
             • To find out how many shots they would make in 30 minutes plug in 30 for X and 60 for K
               • Y=60/30
                 • divide 60 by 30
                   • Then you get 2 shots for the final answer
   • direct
     • The more field goals Jimmy shot, resulted in him making more field goals. If Jimmy shot
       • 40 field goals and made 20, how many field goals would he make if he shot 60?
         • First set up an equation to solve for K. Plug 40 in as y and 20 in as X
           • 40=K20
             • divide both sides by 20
               • and you get 2 for K
                 • To find out how many he would make if he shot 60 plug in 60 for Y and 2 for K
                   • 60=2X
                     • divide both sides by 2 and you get 30 shots for the final answer.

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