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Section 3.3 The Slope of a Line
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Slope In a coordinate plane, the slope of a straight line is defined by the change in y divided by the change in x. (3, 0) x y 1 2 3 4 1 2 3 4 (0, 2) Change in y = 2 Change in x = 3
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Definition of Slope of a Line
The slope of any nonvertical line that contains the points with coordinates (x1, y1) and (x2, y2) is defined by the difference ratio where x2 x1.
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Example Find the slope of the line that passes through (3, 6) and (1, 2).
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Example Find the slope of the line that passes through (3, 2) and (2, 4).
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Example Find the slope of the line that passes through (0, 2) and (5, 2).
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Example Find the slope of the line that passes through (4, 0) and (4, 4).
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Types of Slope Positive Slope Line goes up to the right y
x y 1. Lines with positive slopes go upward as x increases. x y Negative Slope Line goes downward to the right Lines with negative slopes go downward as x increases.
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Types of Slope x y Zero Slope Horizontal Line
Horizontal lines have a slope of 0. Undefined Slope Vertical Line x y A vertical line has an undefined slope.
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Slope-Intercept The slope-intercept form of the equation of a line that has slope m and y-intercept (0, b) is given by y = mx + b. y = 3x – 4 The slope is 3. The y-intercept is (0, -4). The slope is The y-intercept is
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Example What is the slope and the y-intercept of the line 5x + 3y = 2? Solve the equation for y. The y-intercept is (0, 2/3). The slope is -5/3.
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Example Find the equation of the line with slope and y-intercept (0, 5).
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Example Graph the line with slope and y-intercept (0, 2). 3 units down
1 2 3 4 1 2 3 4 (0, 2) 3 units down rise 2 units to the right run (2, 1)
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