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Learn direct and inverse variations in math with examples and formulas. Understand how to solve problems involving direct and inverse relationships between variables. Practice cross multiplication, setting up equations, and solving for unknowns.
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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.
