1 / 6

Direct Variation and Proportion Problems

Learn how to find equations of direct variation, solve problems with direct proportion, and understand the steps involved. Practice problems and solutions included.

ernestwalker
Download Presentation

Direct Variation and Proportion Problems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Variation and Proportion Direct Proportion

  2. The formula for direct variation can be written as y=kx where k is called the constant of variation. • The steps to follow to solve a problem with direct variation: • Write the equation: y = kx • Substitute for x and y • Solve for k • Rewrite the equation with k as the constant

  3. Problem:Find an equation of direct variation where y varies directly as x. One pair of values is y = 7 when x = 35. • Write the equation: y = kx y = kx • Substitute for x and y 7 = k(35) • Solve for k 7/35 = k, or k = 1/5 • Rewrite the equation with k y = 1/5x as the constant

  4. Problem:The cost of operating a TV varies directly as the number (n) of hours it is in operation. It costs $14.00 to operate a standard size color TV continuously for 30 days. • y = cost; x = number of hours • y = kx • 14 = k(30) • 14/30 = k, or k = 7/15 • Equation: • y = 7/15x

  5. Practice Problems: Answers • y = 28 when x = 7 • Equation: y = 4x • y = 30 when x = 8 • Equation: y = 15/4x • y = 400 when x = 125 • Equation: y = 16/5x • y = 630 when x = 175 • Equation: y = 18/5x

  6. Practice Problems: Answers (Continued) • The number (b) of bolts a machine can make varies directly as the time it operates. It can make 6578 bolts in 2 hours. How many bolts can it make in 5 hours? • Set up a proportion: • 6578/2 = x/5 • x = 16445

More Related