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Direct and
Inverse
Variations
Direct Variation
When we talk about a direct
variation, we are talking about
a relationship where as
x increases,
y increa...
Direct Variation
y1
x1
=
y2
x2
Direct variation uses the
following formula:
Direct Variation
example:
if y varies directly as x
and y = 10 as x = 2.4,
find x when y =15.
what x and y go together?
Direct Variation
If y varies directly as x and y = 10
find x when y =15.
y = 10, x = 2.4
make these y1 and x1
y = 15, and ...
Direct Variation
if y varies directly as x and y = 10
as x = 2.4, find x when y =15
10
2.4
=
15
x
Direct Variation
How do we solve this? Cross
multiply and set equal.
10
2.4
=
15
x
Direct Variation
We get: 10x = 36
Solve for x by diving both sides by 10.
We get x = 3.6
Direct Variation
Let’s do another.
If y varies directly with x
and y = 12 when x = 2,
find y when x = 8.
Set up your equat...
Direct Variation
If y varies directly with x and y
= 12 when x = 2, find y when x
= 8.
12
2
=
y
8
Direct Variation
Cross multiply: 96 = 2y
Solve for y. 48 = y.
12
2
=
y
8
Inverse Variation
Inverse is very similar to
direct, but in an inverse
relationship as one value goes
up, the other goes d...
Inverse Variation
With Direct variation we
Divide our x’s and y’s.
In Inverse variation we will
Multiply them.
x1y1 = x2y2
Inverse Variation
If y varies inversely with x and
y = 12 when x = 2, find y when x = 8.
x1y1 = x2y2
2(12) = 8y
24 = 8y
y ...
Inverse Variation
If y varies inversely as x and x = 18
when y = 6, find y when x = 8.
18(6) = 8y
108 = 8y
y = 13.5
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Direct and Inverse variations

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Transcript of "Direct and Inverse variations"

  1. 1. Direct and Inverse Variations
  2. 2. Direct Variation When we talk about a direct variation, we are talking about a relationship where as x increases, y increases or decreases at a CONSTANT RATE.
  3. 3. Direct Variation y1 x1 = y2 x2 Direct variation uses the following formula:
  4. 4. Direct Variation example: if y varies directly as x and y = 10 as x = 2.4, find x when y =15. what x and y go together?
  5. 5. Direct Variation If y varies directly as x and y = 10 find x when y =15. y = 10, x = 2.4 make these y1 and x1 y = 15, and x = ? make these y2 and x2
  6. 6. Direct Variation if y varies directly as x and y = 10 as x = 2.4, find x when y =15 10 2.4 = 15 x
  7. 7. Direct Variation How do we solve this? Cross multiply and set equal. 10 2.4 = 15 x
  8. 8. Direct Variation We get: 10x = 36 Solve for x by diving both sides by 10. We get x = 3.6
  9. 9. Direct Variation Let’s do another. If y varies directly with x and y = 12 when x = 2, find y when x = 8. Set up your equation.
  10. 10. Direct Variation If y varies directly with x and y = 12 when x = 2, find y when x = 8. 12 2 = y 8
  11. 11. Direct Variation Cross multiply: 96 = 2y Solve for y. 48 = y. 12 2 = y 8
  12. 12. Inverse Variation Inverse is very similar to direct, but in an inverse relationship as one value goes up, the other goes down. There is not necessarily a constant rate.
  13. 13. Inverse Variation With Direct variation we Divide our x’s and y’s. In Inverse variation we will Multiply them. x1y1 = x2y2
  14. 14. Inverse Variation If y varies inversely with x and y = 12 when x = 2, find y when x = 8. x1y1 = x2y2 2(12) = 8y 24 = 8y y = 3
  15. 15. Inverse Variation If y varies inversely as x and x = 18 when y = 6, find y when x = 8. 18(6) = 8y 108 = 8y y = 13.5
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