slopes and direct variation december 9, 2010. review slope slope – rise run (-1, -4) and (2, 2)

Slopes and Direct Variation

December 9, 2010

Review Slope

• Slope – Rise

Run

(-1, -4) and (2, 2)

12

12

xx

yy

23

6

21

24

Given a point and slope, find another point

• Given (-7, 7) as our point

and our slope is 4

3



and our slope is 4

3

-3



and our slope is 4

3

-3

4



and our slope is

Our next point is (-3, 4)

4

3

-3

4



and our slope is


Try again

4

3

-3

4 -3



and our slope is


Try again

4

3

-3

4 -3

4



and our slope is


Try again

Our next point is (1, 1)

4

3

-3

4 -3

4

You try

• Point (5, 2) and

slope of 2

1

You try


slope of 2

1

1

You try


slope of 2

1

12

You try


slope of

New Point is (3, 1)

2

1

12

Direct Variation

• Definition-an equation in the form y = kx, where k ≠ 0

• k is the constant of the variation or the constant of proportionality

• k is also the slope of the equation

•What is the constant variation?•The constant is

•Check find the slope

Find slope in equation

2

1

2

1

4

2

04

02

Find the slope

Graph y = x.

Step 1 Write the slope as a ratio. Step 2 Graph (0, 0).Step 3 From the point (0, 0), move up 3 units and right 5 units. Draw a dot.Step 4 Draw a line connecting the points.

Given an equation, graph

5

3

Write and Solve Direct Variation

• Suppose y varies directly as x, and y=63 and x=9y=kx63=k(9)7=k

• Suppose y varies directly as x, and y=72 and x=8 y=kx72=k(8)9=k

Write and Solve Direct Variation

• Suppose y varies directly as x, and y = -10 when x = 8.

• Suppose y varies directly as x, and y = -319 when x = 29.

• If y varies directly as x and y = 21 when x = 5, find x when y = 42.

slopes and direct variation december 9, 2010. review slope slope – rise run (-1, -4) and (2, 2)

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