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3.4 – Slope & Direct Variation

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Direct Variation:

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3.4 – Slope & Direct Variation Direct Variation: y = kx

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3.4 – Slope & Direct Variation Direct Variation: y = kx (k = constant of variation)

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3.4 – Slope & Direct Variation Direct Variation: y = kx (k = constant of variation) Reads:

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3.4 – Slope & Direct Variation Direct Variation: y = kx (k = constant of variation) Reads: “y varies directly with x.”

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3.4 – Slope & Direct Variation Direct Variation: y = kx (k = constant of variation) Reads: “y varies directly with x.” –Direct Variation Equations ALWAYS go through the origin!!!

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3.4 – Slope & Direct Variation Direct Variation: y = kx (k = constant of variation) Reads: “y varies directly with x.” –Direct Variation Equations ALWAYS go through the origin!!! –Constant of Variation = Slope

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3.4 – Slope & Direct Variation Direct Variation: y = kx (k = constant of variation) Reads: “y varies directly with x.” –Direct Variation Equations ALWAYS go through the origin!!! –Constant of Variation = Slope, so k = m!

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Ex. 1 Graph y = 4x

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1)Write the slope as a ratio.

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Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 =

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Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1

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Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0)

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Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0)

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Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0) 3)Use slope to find next point.

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Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0) 3)Use slope to find next point. 4

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Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0) 3)Use slope to find next point. 1 4

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Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0) 3)Use slope to find next point. 1 4

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Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0) 3)Use slope to find next point. 4)Draw line through points 1 4

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Ex. 1 Graph y = 4x 1)Write the slope as a ratio. 4 = 4 1 2)Graph (0,0) 3)Use slope to find next point. 4)Draw line through points 1 4

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Ex. 2 Graph y = -½x

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1)Write the slope as a ratio. 2)Graph (0,0) 3)Use slope to find next point. 4)Draw line through points

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Ex. 2 Graph y = -½x 1)Write the slope as a ratio. 2 2)Graph (0,0) 3)Use slope to find next point. 4)Draw line through points 2

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Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.

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Ex.3 If y = 8 when x= 4, find y when x= 5.

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Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation:

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Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx

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Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4)

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Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k

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Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k k = 2

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Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x

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Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x 2)Plug in given value, solve for missing!

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Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x 2)Plug in given value, solve for missing! y = 2x

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Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x 2)Plug in given value, solve for missing! y = 2x y = 2(5)

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Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve. Ex.3 If y = 8 when x= 4, find y when x= 5. 1)Write equation: y = kx 8 = k(4) 8 = 4k k = 2, so y = 2x 2)Plug in given value, solve for missing! y = 2x y = 2(5) y = 10

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Ex.4 If y = 36 when x = 6, find x when y = 42

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1)Write equation: 2)Plug in given value, solve for missing!

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Ex.4 If y = 36 when x = 6, find x when y = 42 1)Write equation:y = kx 36 = k(6) 36 = 6k k = 6, so y = 6x 2)Plug in given value, solve for missing! y = 6x 42 = 6x 7 = x

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