1 / 12

9.1: Inverse and Joint Variation

9.1: Inverse and Joint Variation. Objectives: Students will be able to… Write and use inverse variation models Write and use joint variation models. Review of Direct Variation:. Linear function whose graph passes through the origin y= kx , where k is the constant of variation

jeanne
Download Presentation

9.1: Inverse and Joint 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. 9.1: Inverse and Joint Variation Objectives: Students will be able to… Write and use inverse variation models Write and use joint variation models

  2. Review of Direct Variation: • Linear function whose graph passes through the origin • y= kx, where k is the constant of variation • “y varies directly with x” (y = kx) • If every is the same for a set of data pairs, then it is direct variation EXAMPLE: • k = y/x = ½ for every data pair • y varies directly with x • y = (1/2) x

  3. Inverse Variation: • “y varies inversely with x” • k = x∙y • If every x∙y is the same for a set of data pairs, then it is inverse variation EXAMPLE: • k = xy= 30 for each data pair • Inverse variation model:

  4. Tell whether x and y show direct variation, inverse variation, or neither. • Solve for y. Does it look like a direct or inverse variation model?? • xy = 4.8 • x = • y –x = 2 Inverse variation Direct variation neither

  5. Does the following show inverse variation, direct variation, or neither? Direct: y = -2x

  6. x and y vary inversely and y = 6 when x = 1.5:a.) write and equation that relates x and yb.) Find y when x = 4/3 a.) Find the constant, k: k = xy k = (1.5)(6) = 9 Write equation using k: b.) Find y when x = 4/3:

  7. YOU TRY: x and y vary inversely and x = 7 when y = 1. Write and equation relating x and y and find y when x = 3.

  8. The volume of gas in a container varies inversely with the amount of pressure. A gas has volume 75 in 3 at a pressure of 25 lb/in2. Write a model relating volume and pressure. “Volume varies inversely with pressure” “ y varies inversely with x “ k = V∙P = 75∙25 k= 1875 V =

  9. Joint Variation: • A quantity varies directly as the product of two or more quantities.

  10. Examples of Variation:

  11. Write and equation for the following: • y varies directly with x and inversely with z2 • y varies inversely with x3 • y varies directly with x2 and inversely with z • z varies jointly with x2 and y • y varies inversely with x and z

  12. The volume of a geometric figure varies jointly with the square of the radius of the base and the height. a.) Write an equation for the volume. b.) Estimate the constant of variation of V = 63.33 in3, r = 2.4 in, and h = 10.5 in.

More Related