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Section 3.3 The Slope of a Line.

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Presentation on theme: "Section 3.3 The Slope of a Line."— Presentation transcript:

1 Section 3.3 The Slope of a Line

2 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

3 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.

4 Example Find the slope of the line that passes through (3, 6) and (1, 2).

5 Example Find the slope of the line that passes through (3, 2) and (2, 4).

6 Example Find the slope of the line that passes through (0, 2) and (5, 2).

7 Example Find the slope of the line that passes through (4, 0) and (4, 4).

8 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.

9 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.

10 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

11 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.

12 Example Find the equation of the line with slope and y-intercept (0, 5).

13 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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