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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
Direct Variation Direct variation uses the following formula:
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 as x = 2.4, find x when y =15 Direct Variation
How do we solve this? Cross multiply and set equal. 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. Direct Variation
Cross multiply: 96 = 2y Solve for y. 48 = y. Direct Variation
We will apply what we know and try this problem. According to Hook’s Law, the force F required to stretch a spring x units beyond its natural length varies directly as x. A force of 30 pounds stretches a certain spring 5 inches. Find how far the spring is stretched by a 50 pound weight.
Set up a proportion Substitute
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
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 = 3 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 Inverse Variation
Lets apply what we have learned. The pressure P of a compressed gas is inversely proportional to its volume V according to Boyle’s Law. A pressure of 40 pounds per square inch is created by 600 cubic inches of a certain gas. Find the pressure when the gas is compressed to 200 cubic inches.
