direct inverse variation
TRANSCRIPT
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
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.
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 “=”)
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 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 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 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?
Direct or Inverse? Direct!So we use y=kx form.
Q: If y directly varies with x and the constant variation is 7. What is the equation for the direct varia-
tion?
Direct or Inverse? Direct!So we use y=kx form.
What does “constant variation” mean? Is it y, k, or x in “y=kx” form? Which part doesn’t change?
Q: If y directly varies with x and the constant variation is 7. What is the equation for the direct varia-
tion?
Direct or Inverse? Direct!So we use y=kx form.
What does “constant variation” mean? Is it y, k, or x in “y=kx” form? Which part doesn’t change?
“k” is the constant value while x and y changes (when you plug different x and y values, k still doesn’t change.
Q: If y directly varies with x and the constant variation is 7. What is the equation for the direct varia-
tion?
Direct or Inverse? Direct!So we use y=kx form.
What does “constant variation” mean? Is it y, k, or x in “y=kx” form? Which part doesn’t change?
“k” is the constant value while x and y changes (when you plug different x and y values, k still doesn’t change.
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
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.
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.
What does “constant variation” mean? Is it y, k, or x in “y=k/x” form? Which part doesn’t change?
“k” is the constant value while x and y changes (when you plug different x and y values, k still doesn’t change.
Q: If y varies inversely with x and the constant variation is 5. What is the equation for the direct varia-
tion?
Direct or Inverse? Inverse!So we use y=k/x form.
What does “constant variation” mean? Is it y, k, or x in “y=k/x” form? Which part doesn’t change?
“k” is the constant value while x and y changes (when you plug different x and y values, k still 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
Direct or Inverse? Inverse!So we use y=k/x form.
Q: If y varies inversely as x and y=2 as x=8, find x when y=4
Direct or Inverse? Inverse!So we use y=k/x form.
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 “=”)
Q: If y varies inversely as x and y=2 as x=8, find x when y=4
Direct or Inverse? Inverse!So we use y=k/x form.
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?
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?
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.
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?
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?
Q: Decide if the information below is a direct or inverse variation?
Write the equation to model the data.
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
Q: Decide if the information below is a direct or inverse variation?
Write the equation to model the data.
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
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
Q: Decide if the information below is a direct or inverse variation?
Write the equation to model the data.
Q: Decide if the information below is a direct or inverse variation?
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
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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