Slopes and Direct Variation December 9, 2010. Review Slope Slope – Rise Run (-1, -4) and (2, 2)

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Presentation transcript:

Slopes and Direct Variation December 9, 2010

Review Slope Slope – Rise Run (-1, -4) and (2, 2)

Given a point and slope, find another point Given (-7, 7) as our point and our slope is

Given a point and slope, find another point Given (-7, 7) as our point and our slope is -3

Given a point and slope, find another point Given (-7, 7) as our point and our slope is -3 4

Given a point and slope, find another point Given (-7, 7) as our point and our slope is Our next point is (-3, 4) -3 4

Given a point and slope, find another point Given (-7, 7) as our point and our slope is Our next point is (-3, 4) Try again -3 4

Given a point and slope, find another point Given (-7, 7) as our point and our slope is Our next point is (-3, 4) Try again

Given a point and slope, find another point Given (-7, 7) as our point and our slope is Our next point is (-3, 4) Try again Our next point is (1, 1)

You try Point (5, 2) and slope of

You try Point (5, 2) and slope of 1

You try Point (5, 2) and slope of 1 2

You try Point (5, 2) and slope of New Point is (3, 1) 1 2

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

Find the slope

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

Write and Solve Direct Variation Suppose y varies directly as x, and y=63 and x=9 y=kx 63=k(9) 7=k Suppose y varies directly as x, and y=72 and x=8 y=kx 72=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.