Direct and Inverse Variation Key

Honors Algebra /Trig Name: KEY Date: Block: 9.1 Direct and Inverse Variation Direct Variation: . x and y show direct variation if k = y/x k is called the constant of variation acts like the slope. Another phrase for "Direct Variation" is directly proportional The graph of goes origin. . . An example formula is d = rt distance rate time Distance and time vary directly, which means as time increases, distance increases OR as time decreases, distance decreases. The variables x and y vary directly. Write an equation that relates the two variables. Then find y when x = underline 6. 1.) x = 2 1 2.) x = 24 k = 1/4 G_{n} = K(24) 3.) x = 0.8 y = - 1.6 y = - 2x - 1.6 = k(0.8) K = - 2 12 Y = - 2(6) = f = K(2) k = 3/2 (E) 9 4.) If y varies directly with x, and when x =2 t then what is the value of y when x =6? 5.) Suppose y is directly proportional to x ^ 2 y = 16 when x = Z_{0} what is the of y when x is 7? k_{o} = k * (2) ^ 2 y = k * x ^ 2 y = 4x ^ 2 )2=4(49) 196 A) 1 8) 2 C) 3 D) 6 16 = 4k when y = 87 6.) If y proportional to x ^ 2 and y = 18 when x = 3 which of the following could be the value of x A) 4 B) 2 C) 1 D) 4/3 E) 6 8 = 9K k = K * (3) ^ 2 y = k * x ^ 2 y = 2x ^ 2 8= 4=x² x=±2 7. ) If y varies directly with x, and y = 24 when x = 8, then what is the value of x when y = 337 24 = K(8) K = overline 3 33 = 3x x = 11 8.) If y varies directly with x, and when x = 13 then what is the value of x when y = 147 52 = K(13) y = 4x y = 52 9.) If y varies directly with the table to the right, then when x = 5.5 what is the value of y? 2 = k(1) or y = 1/5 * x y = 1.1 10.) Which following tables shows a direct variation of y in terms of x? y 1 0.2 2 0.4 3 0.6 4 0.8 3 6 1. Make sure graph passes thru (0,0) 2) Make sure kis Constant: K y Ex 0 0 0 0 0 0 1 0 0 21 1 1 K-101 10 1 3 2 3 X = 2/2 4 K2 15 2 5 3 4 9 20 37 X ^ 3 2 9 doesn't pass thru origin doesn't pass thru origin x = 0.2 = 1/5 14/4 = (4x)/4 x = 7/2 y = 7/5 * (5, 5) k = 1/2 1 = K(2) y = 0.2x \\ =.2(5.5) y = 3/2 * (6) = 9 7y = 3/2 * x y = 1/4 * (6) = boxed 3 2 y = 1/4 * x y = 3x x = 20/3 aligned y=2n]\\ y = 2/2 * (6) = boxed 21 aligned Inverse Variation x and y show inverse variation if y = k/x K = xy Another phrase for "Inverse Variation" is Indirect Variation/Indirectly proportional. An example formula is mass density volume Density and volume vary indirectly, which means as volume increases, density decreases. d = m/v The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 4 11.) y = 6 x = 1.5 12.) y = underline 7.5, y = k/x - 7.5 = K/2 K = 9 6 = K/1.5 y = K/x K = - 15 13.) y = 2 K = 16 y = K/x 2 = K/8 14.) If y is inversely proportional to x, and when x = 2 then what is the value of y when x = 67 (A) 1 B) 2 C) 3 D) 6 E) 9 1 15.) Suppose y varies indirectly to the square of x. When x is 2, y is equal to is the value of y when x is 10? (A) 1 B) 4 C) 5 D) 10 E) 25 K=100 100 X 16.) If y varies inversely with x and y = 4 when x = 2 then which of the following defines y in terms of x? Choose all that apply. y = 2x ) xy = 8 y = 8/x 001 100 10 100 100 17.) If indirectly with x ^ 2 and y = 9 when x = 3 then what is the value of x when y = 187 18 = 81/(x ^ 2) 18x ^ 2 = 81 18.) Which of the following expresses a relationship where y is inversely proportional to x? 1 4 3 9 4 16 X = 1 54 K108 3 36 V = 10R K=21 2 3 4 4 5 k = 29 2 10 3 3 5 4 7 x <= 1 3 15 4 20 Make sure k is constant. K = xy Direct variation, Inverse variation or Neither? Isolate y! 19.) xy = 4.8 Inverse y = 4.8/x 20.) x = y/1.5 y = 1.5x Direct 21.) y= 2x + ) 22.) x = 3y Neither Direct y = x/3 -> y = 1/3 * x x = (plus/minus 3 * sqrt(2))/2 x = plus/minus sqrt(9/2) = plus/minus 3/(sqrt(2)) * (sqrt(2))/(sqrt(2)) zeta( y = 2/x y = k/x 3 = k/2 y = 8x y = K/(x ^ 2) 9 = K/(3 ^ 2) x = 8/x y = 9/4 K = 6 integrate 7x ^ 2 = 81/18 dx K = 8 y = K/X 4 = x/2 \\ w-2 aligned y = 16/x y = - 15/4 x ^ 2 = 9/2 y = 9/x y = 81/(x ^ 2) y = 16/4 -> sqrt(y = 4) Y = 1 25 = k/(k ^ 2) q = 5/9 k = 81