Direct and Inverse Variations. 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. Direct Variation. Direct variation uses the following formula:. example:
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When we talk about a direct variation, we are talking about a relationship where as x increases, y increasesor decreases at a CONSTANTRATE.
Direct variation uses the following formula:
example: a relationship where as
if y varies directly as x and y = 10 as x = 2.4, find x when y =15.
what x and y go together?
If y varies directly as x and y = 10 a relationship where as find x when y =15.
y = 10, x = 2.4 make these y1 and x1
y = 15, and x = ? make these y2 and x2
We get: 10x = 36 y =15
Solve for x by diving both sides by 10.
We get x = 3.6
Let’s do another. y =15
If y varies directly with x and y = 12 when x = 2, find y when x = 8.
Set up your equation.
Cross multiply: 96 = 2y when x = 8.
Solve for y. 48 = y.
Inverse when x = 8. 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.
With when x = 8.Direct variation we Divide our x’s and y’s.
In Inverse variation we will Multiply them.
x1y1 = x2y2
If y varies inversely with x and when x = 8.y = 12 when x = 2, find y when x = 8.
x1y1 = x2y2
2(12) = 8y
24 = 8y
y = 3
18(6) = 8y
108 = 8y
y = 13.5