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Section 2.3 Linear Functions: Slope, Graphs & Models. 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. - PowerPoint PPT Presentation
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2.3 1
Section 2.3Linear Functions: Slope, Graphs & Models
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.
xinchange
yinchange
x
ym
2.3 2
What is Slope & Why is it Important?
Using any 2 points on a straight line will compute to the same slope.
2.3 3
The Dope on Slope 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:
Horizontal lines (like y = 3 ) have slope 0 Vertical lines (like x = -5 ) have an undefined slope Parallel lines have the same slope m1 = m2
Perpendicular lines have negative reciprocal slopes m1=-1/m2
21
21
12
12
xxyy
xxyy morm
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Slope Intercept Form of a Straight Line f(x) = mx + b or y = mx + b
Both lines have the same slope, m = 2
2.3 5
Using b to identify the y-intercept point (0,b)
the above y-intercepts are: (0,0) and (0,-2) What’s the y-intercept of y = -5x + 4 (0,4) What’s the y-intercept of y = 5.3x - 12 (0,-12)
2.3 6
Calculating Slopes
2.3 7
Graphing a Straight Line using the y-intercept and the slope
2.3 8
The Slope-Intercept Form of a Line
2.3 9
Graphing Practice:
2.3 10
Lines not in slope-intercept form
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2.3 15
Next Section 2.4 Another Look at Linear Graphs