3.4 – Slope & Direct Variation. Direct Variation:

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Presentation transcript:

3.4 – Slope & Direct Variation

Direct Variation:

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

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

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

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

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!!!

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

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!

Ex. 1 Graph y = 4x

1)Write the slope as a ratio.

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

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

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

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

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.

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

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

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

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

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

Ex. 2 Graph y = -½x

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

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

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.

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:

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

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)

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

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

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

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!

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

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)

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

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

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

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