1 / 11

Direct Variation

Direct Variation. 5-2. What is a Direct Variation?. A special equation in the form: y = kx k is called the “constant of variation”; it is also the slope of the equation The variables have a direct relationship; as one increases/decreases, so does the other

francesmorris
Download Presentation

Direct Variation

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. Direct Variation 5-2

  2. What is a Direct Variation? • A special equation in the form: y = kx • k is called the “constant of variation”; it is also the slope of the equation • The variables have a direct relationship; as one increases/decreases, so does the other • The graph of a direct variation always passes through the origin

  3. Determining a Direct Variation FROM EQUATIONS: • Put equation into form (y = ) and determine if it fits the pattern y = kx Are these direct variations? y = x y = 2x – 1 3x = 5y

  4. Determining a Direct Variation FROM TABLES: • Solve each ordered pair for k (k = y/x) • If k is constant for each ordered pair, you have a direct variation

  5. Examples

  6. Graphing Direct Variations • Always know 1 point on the line: (0,0) • Use k (the slope) to get additional points

  7. Examples Graph: y = -3x Graph:

  8. Writing Direct Variation Equations • Substitute variables into direct variation equation, y = kx • Solve for k • Write the direct variation equation with k

  9. Examples Write a direct variation eq’n for x = 4 and y = 12. Write a direct variation eq’n for x = -9 and y = 3.

  10. Direct Variation Word Problems • Determine which value is x and which is y • Remember y varies directly with x • Substitute information into direct variation equation • Solve for k • Rewrite equation with k • If needed, substitute remaining information to solve for the required variable

  11. Example Mary’s salary varies directly with the number of hours she works. If Mary’s salary is $273 when she works 28 hours, write a direct variation equation relating these variables. How many hours would she have to work to earn $351?

More Related