slopes and direct variation december 9, 2010. review slope slope – rise run (-1, -4) and (2, 2)
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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
Given a point and slope, find another point
• Given (-7, 7) as our point
and our slope is 4
3
-3
Given a point and slope, find another point
• Given (-7, 7) as our point
and our slope is 4
3
-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)
4
3
-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
4
3
-3
4 -3
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
4
3
-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
Our next point is (1, 1)
4
3
-3
4 -3
4
You try
• Point (5, 2) and
slope of 2
1
You try
• Point (5, 2) and
slope of 2
1
1
You try
• Point (5, 2) and
slope of 2
1
12
You try
• Point (5, 2) and
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.
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