Direct inverse variation

Direct or Inverse Varia-tion?

Direct Variation

• Y=kx, where k is the constant rate of change. • As x increases, y increases. • Graph passes through the origin and is straight line.

http://www.austintown.k12.oh.us/~aust_hmw/08-09/math/2010-01-06%20Direct%20&%20Inverse%20Variation.pdf

Q: If y directly varies as x and y=10 as x=2, find x when y=20

Direct or Inverse? Direct!So we use y=kx form.



Coordinate of the first point is (2,10)Plug them in the y=kx form. 10 = 2k, so k=5. Now the full equation is y=5x. (remember equation? You need “=”)



Coordinate of the first point is (2,10)Plug them in the y=kx form. 10 = 2k, so k=5. Now the equation is y=5x. (remember equation? You need “=”)

Now we need to find x value when y=20Again, plug them in y=5x again. We don’t know x, so leave x as it is. 20=5∙x Divide each side with 5 to get rid of 5 (we want only x in the right side)20/5 = x, so x=4

Q: If y directly varies with x and the constant variation is 7. What is the equation for the direct varia-

tion?



tion?


What does “constant variation” mean? Is it y, k, or x in “y=kx” form? Which part doesn’t change?


tion?



“k” is the constant value while x and y changes (when you plug different x and y values, k still doesn’t change.


tion?




So k=7! Let’s plug k into the equation form. The answer is “y=7x”

Inverse Variation

• Y=k/x, where k is the constant rate of change. • As one quantity increases, the other decreases. • Always two curves, which never touch

neither x-axis nor y-axis..

http://www.austintown.k12.oh.us/~aust_hmw/08-09/math/2010-01-06%20Direct%20&%20Inverse%20Variation.pdf

Q: If y varies inversely with x and the constant variation is 6. What is the equation for the direct varia-

tion?

Direct or Inverse? Inverse!So we use y=k/x form.


tion?


What does “constant variation” mean? Is it y, k, or x in “y=k/x” form? Which part doesn’t change?



tion?


What does “constant variation” mean? Is it y, k, or x in “y=k/x” form? Which part doesn’t change?


So k=5! Let’s plug k into the equation form. The answer is “y=5/x”

Q: If y varies inversely as x and y=2 as x=8, find x when y=4




Coordinate of the first point is (2,8)Plug them in the y=k/x form. 8=k/2, so k=16.Now the equation is y=16/x. (remember equation? You need “=”)



Coordinate of the first point is (2,8)Plug them in the y=k/x form. 8=k/2, so k=16.Now the equation is y=16/x. (remember equation? You need “=”)

Now we need to find x value when y=4Again, plug them in y=16/x again. We don’t know x, so leave x as it is. But we do have y. y=44=16/x Multiply each side with x to move x to the left. 4∙ x=16. Now divide each side with 4 to leave only x in the left.x = 16/4 = 4

Q: Decide if the information below is a direct or inverse variation?

Write the equation to model the data.

X 2 7 10

y 35 10 7

When x increase, what happens in y? Y decreases. So is it direct or inverse variation?



X 2 7 10

y 35 10 7


It is an Inverse variation! So what is the form of equation?y=k/xLet’s plug the first set of values: x=2, y=3535 = 2/k, so k=70.



X 2 7 10

y 35 10 7


It is an Inverse variation! So what is the form of equation?y=k/xLet’s plug the first set of values: x=2, y=3535 = 2/k, so k=70.

Now let’s complete the equation. y=70/x

X 5 6 8

y 55 66 88

When x increase, what happens in y? Y increases too. So is it direct or inverse variation?




Direct Variation!What is the form of equation?y=kx

X 5 6 8

y 55 66 88





Let’s plug the first set in the equation to x=5, y=5555=5∙x, so k=11

X 5 6 8

y 55 66 88




X 5 6 8

y 55 66 88



Let’s plug the first set in the equation to x=5, y=5555=5∙x, so k=11

Let’s plug k back in the equationy=11x

Now ready to do the Warm-up ques-tions?

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Direct inverse variation

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