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8-1/2-2 Direct and Inverse Variation

Learn about direct and inverse variation equations, solve for constants, and determine relationships between variables through practical examples and solutions.

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8-1/2-2 Direct and Inverse Variation

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  1. 8-1/2-2 Direct and Inverse Variation

  2. Direct Variation Inverse Variation Equation: y = k/x Solve for constant “k” k = xy As x increases, y decreases As x decreases, y increases Equation: y = kx Solve for constant “k” k = y/x As x increases, y increases As x decreases, y decreases

  3. Ex 1)Determine whether y varies directly or indirectly with x. If so, find the constant Question Answers Indirect, k =10 Neither Direct, k = 2 • a. • b. c.

  4. y = kx Ex 2) Determine whether y varies Directly or indirectly with x.if so, write the equation. y = k/x =30 =40 =20 =30 =40 =32 =30 =40 =30 =30 =40 =22.5 Yes! y = 30/x Yes! y = 40x No! Neither Inverse? Check constant k = xy Direct? Check constant k = y/x Inverse? Check constant k = xy

  5. Ex 3) Write a direct variation that passes through each point y = kx • a. (5,4) • b.(8,-3) Find constant k = y/x Plug into equation y = kx

  6. y = k/x Ex 4) Write an inverse variation that passes through each point • a. (7, 11) • b. (-3, -6) Find constant k = xy Plug into equation y = k/x

  7. y = kx Ex 5) • Suppose y varies directly with x and y = 9 when x = -15. Write an equation and find what y is when x = 21. Find constant: k = y/x = 9/-15 = -3/5 Write Equation: y = kx=y = (-3/5)x When x = 21, then y = kx= y = (-3/5)(21) y = -63/5 Find constant k = y/x Plug into equation y = kx

  8. y = k/x Ex 5) b) Suppose y varies inversely with x and x = 4 when y = 12. Write an equation and find what y is when x = 10. Find constant: k = xy= 4(12) = 48 Write Equation: y = k/x =y = 48/x When x = 10, then y = k/x = y = 48/10 y = 24/5 Find constant k = xy Plug into equation y = k/x

  9. Find constant k = y/x Plug into equation y = kx Ex 5 continued - T.O.O. c) Suppose y varies directly with x and y = 15 when x = 3. Write an equation and find what y is when x = 12. d) Suppose y varies inversely with x and x = 8 when y = -7. Write an equation and find what y is when x = 2. Answers c) y = 5x; If x = 12, then y = 60 d) y = -56/x; If x = 2, then y = -28 Find constant k = xy Plug into equation y = k/x

  10. 3 Variables EX 6) Suppose z varies directly with x and inversely with y and that z = 15 when x = 6 and y = 2. Write an equation and determine what z is when x = 4 and y = 9. Find k. Write equation. Find z.

  11. Ex7) T.O.O • Suppose z variesinversely with the (product of x and y) and z = 0.5 when x = 2 and y = 4. Write an equation and find what z is when x = 4 and y = 9. • Write a direct variation for (-2,3) and use it to find the missing coordinate of (x,6). • Write an inverse variation for (-2,3) and use it to find the missing coordinate of (x,6). Answers • z = 4/(xy), z = 1/9 • y = (-3/2)x, x = -4 • y = -6/x, x = -1

  12. Homework • W-S 8-1/2-2

  13. TOD • Given (3, 5) find BOTH the direct and indirect variation. Then, solve both equations use x=-9 and solve for x. • Direct variation equation • Direct variation answer -15 • Indirect variation equation • Indirect variation answer -5/3

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