3.4 – Slope & Direct Variation

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

Ex. 1 Graph y = 4x1) Write the slope as a ratio.

Ex. 1 Graph y = 4x1) Write the slope as a ratio.

4 =

Ex. 1 Graph y = 4x1) Write the slope as a ratio.

4 = 4

1

Ex. 1 Graph y = 4x1) Write the slope as a ratio.

4 = 4

1

2) Graph (0,0)

Ex. 1 Graph y = 4x1) Write the slope as a ratio.

4 = 4

1

2) Graph (0,0)

Ex. 1 Graph y = 4x1) Write the slope as a ratio.

4 = 4

1

2) Graph (0,0)

3) Use slope to find next

point.

Ex. 1 Graph y = 4x1) 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 = 4x1) 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 = 4x1) 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 = 4x1) 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 = 4x1) 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

Ex. 2 Graph y = -½x1) 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 = -½x1) Write the slope as a ratio.

-1

2

2) Graph (0,0)

3) Use slope to find next

point.

4) Draw line through points

-1

2

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

• 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 = 2x2) 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 = 2x2) 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

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 = 6x2) Plug in given value, solve for missing!

y = 6x 42 = 6x

7 = x