classroom assignment
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![Page 1: Classroom Assignment](https://reader033.vdocuments.us/reader033/viewer/2022061212/5494b41db47959962d8b5a01/html5/thumbnails/1.jpg)
Slope and Rates of Change
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Essential Questions
• How can I determine the steepness of a line?
• How can I represent the slope on a coordinate plane?
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Georgia Performance Standard
• GA-GPS.M7A3: Students will understand relations and functions.
• GA-GPS.M7A3(b): Represent, describe and analyze a functional relation from a table, graph, and/or formula.
• GA-GPS.M7A3(c): Describe the variation of two quantities
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SLOPE• Is a measurement of a line’s
steepness• Ratio of rise to run
x
Run
RiseRise
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• line points upward as x increases, its slope is positive
• line points downward as x increases, its slope is negative
Positive
0
y
x
Negative Neither
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Example 1Tell whether the slope is positive or negative. Then find the slope.
3
3
slope = riserun
= 33
= 1
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Example 2Tell whether the slope is positive or negative. Then find the slope.
2
-3
0 2
2
–2–2
y
x
slope = riserun
= 2 -3
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Example 3
M(1, –1) N(3, –1)
2
Tell whether the slope is positive or negative. Then find the slope.
slope = riserun
= 02
= 0
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Example 4
(0, –4)
(–2, 4)
8
–2
slope = 8–2 = –4
Tell whether the slope is positive or negative. Then find the slope.
Negative.
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Example 5You can graph a line if you know its
slope and one of its points.Use the slope - and the point (1, –1) to graph the line.
2 1
y
x–4
–4
4
4
0 2
2
–2–2
= orriserun
-2 1
2-1
●
●
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• The ratio of two quantities that change, such as slope, is a rate of change.
• A constant rate of change describes changes of the same amount during equal intervals. The graph of a constant rate of change is a line.
• A variable rate of change describes changes of a different amount during equal intervals. the graph of a variable rate of change is not a line.
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Example 7
Tell whether each graph shows a constant or variable rate of change.
A. B.
The graph is nonlinear,so the rate of change is variable.
The graph is linear, so the rate of change isconstant.
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Example 8Tell whether each graph shows a constant or variable rate of change.
A. B.
The graph is nonlinear,so the rate of change is variable.
The graph is linear, so the rate of change isconstant.
y
x–4
–4
4
4
0 2
2
–2–2
y
x–4
–4
4
4
0 2
2
–2–2
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Tell Whether the graphs are variable or constant
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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Constant or Variable
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AssessmentSlope Poetry
• Students will create a poem that explains the rise over run relationship
• Include an illustration with your poem