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section21

# section21 - MAT 111 College Algebra Chapter 2 Functions and...

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MAT 111 - College Algebra Chapter 2 Functions and Their Graphs Section 2.1: Linear Equations in Two Variables Linear equations in two variables may have one of the following forms: 1. Slope-intercept form. 2. Two-point form. 3. Point-slope form. 4. General form. Graphs of linear equations are straight lines. 1. Slope-Intercept Form: Equation of a non-vertical line may have the form y = mx + b, where m and b are real numbers . b is the . . . -intercept . m is the slope of the line; that is, the rise / fall run . If line is vertical, then slope is . . . . Equation of a vertical line is : If line is horizontal, then slope is . . . . Equation of a horizontal line is: To graph a linear equation we need only two points: one is (0, b ) and the second point can be obtained either by (a) picking another value of x and finding the corresponding y value. (b) Or using the slope.

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Example: Graph x + y = 2. Finding the Slope: (a) Given equation of a line, write the equation in slope-intercept form. (b) Given two points ( x 1 , y 1 ) and ( x 2 , y 2 ), the slope m = Example: Find the slope of the line passing through the points (2, 4) and (4, -4) and write
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