rate of change and slope - madison county school district · 2010-04-26 · rate of change and...
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![Page 1: Rate of Change and Slope - Madison County School District · 2010-04-26 · Rate of Change and Slope Chapter 6 –Linear Equations. Warm Up for 11/12/08 Lesson Quiz 5-1. Rate of Change](https://reader036.vdocuments.mx/reader036/viewer/2022070912/5fb43887e7343c64b854b130/html5/thumbnails/1.jpg)
Rate of Change and Slope
Chapter 6 – Linear Equations
![Page 2: Rate of Change and Slope - Madison County School District · 2010-04-26 · Rate of Change and Slope Chapter 6 –Linear Equations. Warm Up for 11/12/08 Lesson Quiz 5-1. Rate of Change](https://reader036.vdocuments.mx/reader036/viewer/2022070912/5fb43887e7343c64b854b130/html5/thumbnails/2.jpg)
Warm Up for 11/12/08
� Lesson Quiz 5-1
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Rate of Change
� A rate of change is a ratio that shows a change in one quantity with respect to a change in another quantity.
_ _ _ _ var_ _
_ _ _ _ var
change in the dependent iableRate of Change
change in the independent iable=
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Rate of Change
� Example
� Find the rate of change for both Greg and
Monica.� Keep in mind that
the earnings are
dependent on the
hours worked
20164
15123
1082
541
MonicaGreg
Earnings ($)Hours Worked
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Rate of Change
workedhoursinchange
earningsinchangechangeofRate
___
____ =
20164
15123
1082
541
MonicaGreg
Earnings ($)Hours Worked
1
4
___
__=
workedhoursinchange
earningsinchange
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Slopes are commonlyassociated with mountains.
![Page 7: Rate of Change and Slope - Madison County School District · 2010-04-26 · Rate of Change and Slope Chapter 6 –Linear Equations. Warm Up for 11/12/08 Lesson Quiz 5-1. Rate of Change](https://reader036.vdocuments.mx/reader036/viewer/2022070912/5fb43887e7343c64b854b130/html5/thumbnails/7.jpg)
The slope we are studying is associated with the graph of a line.
Slope
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Slope
� When you graph a straight line, it’s going to look like you’re either going up a mountain slope or down a mountain slope.
� Positive slope – uphill
� Negative slope - downhill
![Page 9: Rate of Change and Slope - Madison County School District · 2010-04-26 · Rate of Change and Slope Chapter 6 –Linear Equations. Warm Up for 11/12/08 Lesson Quiz 5-1. Rate of Change](https://reader036.vdocuments.mx/reader036/viewer/2022070912/5fb43887e7343c64b854b130/html5/thumbnails/9.jpg)
Slope
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Slope Definitions
� Slope is the change in y versus the change in x.
� .
� .
� When you graph a line, if you start at one point, you have to go up and over (or down and back) to get to the next point.
xinChange
yinChange
__
__
Run
Rise
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Graph (3,2) and (-1,-1)
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Draw a line through the points.
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Now that we have our line lets find its slope.
Remember we are finding the following ratio:
Vertical or Rise
Horizontal Run
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Vertical Change
or the Rise
3
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Horizontal Changeor the Run
4
3
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Vertical RiseHorizontal Run
3
4
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Find the slope of the following line.
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The slope is…
1
2
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Find the slope of the line.
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The slope is….
-3
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Find the slope of these lines.
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The slope is…
� Black line 3
� Red Line 1
� Blue Line -1/2
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Find the slope of these lines
![Page 24: Rate of Change and Slope - Madison County School District · 2010-04-26 · Rate of Change and Slope Chapter 6 –Linear Equations. Warm Up for 11/12/08 Lesson Quiz 5-1. Rate of Change](https://reader036.vdocuments.mx/reader036/viewer/2022070912/5fb43887e7343c64b854b130/html5/thumbnails/24.jpg)
The slope is…
� Orange line0
� Green Line Undefined
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Finding Slope
� Given (-2, 0) and (1,3), find the slope.
� 0 - 3 = -3/-3 = 1 =
� -2 – 1
� If I start at (-2, 0), I have to go up 1 and to the right 1 to get closer to (1,3)
xinChange
yinChange
__
__
1
1
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Let’s draw a line using slope.
What else do you think you need besides the slope in order to draw a line?
A point!
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If you know the slope and one point on the line you can draw the line.Example: slope is 1/3 and the point (-2,-1)
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Now you draw a line.
� Given: slope is 2/3 and the point is (1,0)
� Given: slope is –3 and the point is (–2,4)
� Given: slope is 1 and the point is (2,3)
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The graphs are…
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Homework for 11/12/08
� Book pages 287 – 288; #28 – 62, even