Published on April 8, 2014
Direct and Inverse Variations
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 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 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 2.4 = 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 equation.
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 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
Direct and Inverse Variation. y varies directly with x (or: "x and y are directly proportional") if there is a constant k such that (You can put the "k" on ...
Sal explains what it means for quantities to vary directly or inversely, and gives many examples of both types of variation.
Type: Resource Title * graphing calculator reference: Lesson: Direct Variation: Lesson: Inverse Variation: Practice: Practice Solving Direct and Inverse ...
Direct variation describes a simple relationship between two variables. We say y varies directly with x (or as x, in some textbooks) if:
Explains the basic terminology of variation problems, and demonstrates how to solve symbolic variation problems.
Inverse Variation (The Opposite of Direct Variation) In an inverse variation, the values of the two variables change in an opposite manner ...
Direct and Inverse Variations Direct Variation When we talk about a direct variation, we are talking about a relationship where as x increases, y increases ...
Understanding direct and inverse variation Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/alge ...
Fun math practice! Improve your skills with free problems in 'Identify direct variation and inverse variation' and thousands of other practice lessons.