Section 2.3
Linear Functions: Slope, Graphs & Models
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y change in y
m
x change in x
Slope
Slope-Intercept Form y = mx + b
Graphing Lines using m and b
Graphs for Applications
Graph paper required for this and all future
graphing exercises. Each graph about 4 inches
square. Limit 6 graphs per page.
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What is Slope & Why is it Important?
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Using any 2 points on a straight line will
compute to the same slope.
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The Dope on Slope
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On a graph, the average rate of change is
the ratio of the change in y to the change in x
For straight lines, the slope is the rate of change between any 2
different points
The letter m is used to signify a line’s slope
The slope of a line passing through the two points (x1,y1) and
(x2,y2) can be computed: m  yx  xy or m  yx  xy
2
1
1
2
2
1
1
2
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Horizontal lines (like y = 3 ) have slope 0
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Vertical lines (like x = -5 ) have an undefined slope
Parallel lines have the same slope m1 = m2
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Perpendicular lines have negative
reciprocal slopes m1=-1/m23
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Slope Intercept Form of a Straight Line
f(x) = mx + b
or
y = mx + b
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Both lines have the same slope,
m=2
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Using b to identify the y-intercept point (0,b)
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the above y-intercepts are: (0,0) and (0,-2)
What’s the y-intercept of y = -5x + 4
(0,4)
2.3 5.3x - 12
What’s the y-intercept of y =
(0,-12)
5
Calculating Slopes
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Graphing a Straight Line using
the y-intercept and the slope
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The Slope-Intercept Form of a Line
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Graphing Practice:
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Lines not in slope-intercept form
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Next
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Section 2.4 Another Look at Linear Graphs
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