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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

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What is Slope & Why is it Important?

Using any 2 points on a straight line will compute to the same slope.

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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

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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)

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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 Section 2.4 Another Look at Linear Graphs