Direct Variation Lesson 2-3.

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Presentation transcript:

Direct Variation Lesson 2-3

= and are both equal to –3, but = 3. Direct Variation Lesson 2-3 Additional Examples For each function, determine whether y varies directly with x. If so, find the constant of variation and write the equation. x –1 2 5 y 3 –6 15 a. = and are both equal to –3, but = 3. y x 3 –1 –6 2 15 5 Since the three ratios are not all equal, y does not vary directly with x. x 7 9 –4 y 14 18 –8 b. = 2, so y does vary directly with x. y x 14 7 18 9 –8 –4 = The constant of variation is 2. The equation is y = 2x.

Determine whether y varies directly with x. If so, write the equation.

5x = –2y is equivalent to y = – x, so y varies directly with x. Direct Variation Lesson 2-3 Additional Examples For each function, tell whether y varies directly with x. If so, find the constant of variation. a. 3y = 7x + 7 Since you cannot write the equation in the form y = kx, y does not vary directly with x. b. 5x = –2y 5x = –2y is equivalent to y = – x, so y varies directly with x. 5 2 The constant of variation is – . 5 2

a. Find the constant of variation. Direct Variation Lesson 2-3 Additional Examples The perimeter of a square varies directly as the length of a side of the square. The formula P = 4s relates the perimeter to the length of a side. a. Find the constant of variation. The equation P = 4s has the form of a direct variation equation with k = 4. b. Find how long a side of the square must be for the perimeter to be 64 cm. P = 4s Use the direct variation. 64 = 4s Substitute 64 for P. 16 = s Solve for s. The sides of the square must have length 16 cm.

15(18) = 27(y) Write the cross products. Direct Variation Lesson 2-3 Additional Examples Suppose y varies directly with x, and y = 15 when x = 27. Find y when x = 18. Let (x1, y1) = (27, 15) and let (x2, y2) = (18, y). Write a proportion. y1 x1 y2 x2 = Substitute. = 15 27 y 18 15(18) = 27(y) Write the cross products. y = Solve for y. 15 • 18 27 y = 10 Simplify.

Find the missing value for the direct variation: If y = 4 when x = 3, what is y when x = 6?