1 / 15

Lesson 7& 8

Lesson 7& 8. Unit 5. Objectives. Be able to find equations for direct variation: y = kx Be able to find equations for inverse variation: y = k/x Be able to find equations for joint variation z = kxy Be able to apply models using variation Vocabulary: constant of proportionality,

enye
Download Presentation

Lesson 7& 8

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. Lesson 7& 8 Unit 5

  2. Objectives • Be able to find equations for direct variation: y = kx • Be able to find equations for inverse variation: y = k/x • Be able to find equations for joint variation z = kxy • Be able to apply models using variation Vocabulary: constant of proportionality, k = constant

  3. HW Read p. 179 – 182 Do p. 182: 1 – 16 all; 17 – 27 odd Do p. 183: 29, 31, 32, 33, 40

  4. Review • Is the equation below in Standard form, slope-intercept form or point-slope form? y = -3x – 11 slope-intercept form • What is the slope of the graph of the equation? slope or m = -3 3. What are the coordinates of the y-intercept? (0, -11)

  5. Review • Write the equation in slope-intercept form for the line that has a slope of 5 and a y-intercept with coordinates (0,0) y = 5x + 0 or y = 5x • What is the equation for a line with a slope of k and y-int of 0? y = kx + 0 or y = kx

  6. New: Direct Variation Definition: “a mathematical model in which one quantity is a constant multiple of the other” • Simply put, this means the equation for direct variation is y = kx. The k is called the constant of proportionality. • The slope of the line is k; the y-int is (0,0) • Direct variation means as x increases, y also increases • Other expressions that mean direct variation are: a) y varies directly as x b) y is directly proportional to x c) y is proportional to x

  7. New: Direct Variation 4. For example, if you earn $7.00 per hour at your job, the amount you earn varies directly with the number of hours worked (varies directly means as hours increase, the amount increases) Let y = the amount, x = the number of hours, and 7 is k or the constant of proportionality, then: y = 7x a) If you work 0 hours, you earn $0; point (0, 0) is on the graph of the line. b) If you work 8.5 hours, you earn $59.50; point (8.5, 59.5) is on the graph of the line

  8. New: Direct Variation • How far you can drive a car depends or varies directly to the number of hours you drive. If d stands for distance and h stands for the hours you drive, what would the equation be? a) Since it is direct variation, then it has to be in the form of y = kx b) So, d = kh (continue on next slide)

  9. New: Direct Variation The piece of information you do not have is k or the constant of proportionality. In this case, k would be the average speed. You can find k though if you know how far you drove and how long it took. If you drove 200 miles and it took 4.5 hours, then d = kh becomes 200 = k(4.5)  k = 200/4.5  k = 44.4 So, the equation is d = 44.4h

  10. New: Direct Variation • Last example: Write the equation that expresses the statement “r varies directly or is proportional to t”if r = 4 when t = 12. a) Direct variation means y = kx b) So, for this example, r = kt c) To find k, we know (4, 12) is a point on the line; it makes the equation true d) So, 12 = 4k  k = 12/4  k =3 e) Finally, the equation is r = 3t

  11. New: Inverse Variation • Similarly to direct variation, inverse variation has a consistent equation: y = k/x • With inverse variation, as x increases, y decreases • k is still the constant of proportionality • Other expressions that mean the same thing: a) y is inversely proportional to x b) y varies inversely as x

  12. New: Inverse Variation • Example: write the equation if g is inversely proportional to h and g = 16 when h = 3 a) Inverse variation means y = k/x b) So, g = k/h c) To find k, substitute and solve: 16 = k/3  3*16 = k  k = 48 d) Finally, g = 48/h

  13. New: Joint Variation Joint variation means that there are more than two quantities (such as x and y) related. In other words, there could be three quantities, such as x, y and z For example: a) if z is directly related to x and y, then z = kxy b) if z is directly related to x and inversely proportional to y, then z =(kx)/y

  14. New: Joint Variation Remember: if a quantity is directly proportional to another quantity, then k is multiplied if a quantity is inversely related to another, then k is divided to find k, plug in the coordinates (x, y) for a point on the line

More Related