Download - Direct and inverse variations
Direct and Inverse
Variations
Variation in general , will concern two variables; say height and weight of a person, and how , when one of these changes, the other might be expected to change.
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.
Direct variation We have Direct Variation, if the two
variables change in the same sense, that is, if one increases, so does the other.
An increase or decrease in one quantity with a corresponding increase or decrease in another quantity such that the ratio remains constant is called direct variation.
Direct Variation
y1x1
y2x2
Direct variation uses the following formula:
Direct Variationexample:
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 VariationIf 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
Direct Variation
if y varies directly as x and y = 10 as x = 2.4, find x when y =15
10
2.415
x
Direct Variation
How do we solve this? Cross multiply and set equal.
10
2.415
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 equation.
Direct Variation
If y varies directly with x and y = 12 when x = 2, find y when x = 8.
12
2y
8
Direct Variation
Cross multiply: 96 = 2ySolve for y. 48 = y.
12
2y
8
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.
Inverse Variation When two quantities vary inversely,
an increase in one leads to the decrease in the other quantity and vice-versa, in inverse ratio.
We have inverse variation if one going up causes the other to go down. An example of this might be speed & time to do a particular journey.
Inverse Variation
With Direct variation we Divide our x’s and y’s. In Inverse variation we will Multiply them.
x1y1 = x2y2
Inverse VariationIf 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
Inverse VariationIf y varies inversely as x and x = 18 when y = 6, find y when x = 8.
18(6) = 8y 108 = 8y y = 13.5