SECTION 1.5 Lines 37 Finding the Point–Slope Form of an Equation of a Line Find the point-slope form of an equation of the line with slope 4, containing the point ( ) 1, 2 . Solution EXAMPLE 4 An equation of the line with slope 4 that contains the point ( ) 1, 2 can be found by using the point-slope form with = = m x 4, 1, 1 and = y 2. 1 ( ) ( ) − = − − = − y y m x x y x 2 4 1 1 1 = = = m x y 4, 1, 2 1 1 See Figure 58 for the graph. Now Work PROBLEM 33 Finding the Equation of a Horizontal Line Find an equation of the horizontal line containing the point ( ) 3, 2 . Solution EXAMPLE 5 Because all the y -values are equal on a horizontal line, the slope of a horizontal line is 0. To get an equation, use the point-slope form with = = m x 0, 3, 1 and = y 2. 1 ( ) ( ) − = − − = ⋅ − − = = y y m x x y x y y 2 0 3 2 0 2 1 1 = = = m x y 0, 3, 2 1 1 See Figure 59 for the graph. Figure 58 ( ) − = − y x 2 4 1 x y 22 5 (1, 2) (2, 6) 6 Run 5 1 Rise 5 4 Example 5 suggests the following result: Figure 59 = y 2 (3, 2) x y –1 1 3 5 4 5 Use the Slope-Intercept Form of a Line Another useful equation of a line is obtained when the slope m and y -intercept b are known.Then the point ( )b 0, is on the line. Using the point-slope form, equation (2), we obtain ( ) − = − = + y b m x y mx b 0 or THEOREM Equation of a Horizontal Line A horizontal line is given by an equation of the form = y b where b is the y -intercept. For example, if a line has slope 5 and y -intercept 2, we can write the equation in slope-intercept form as = + y x5 2 ↑ ↑ slope y -intercept Now Work PROBLEMS 53 AND 59 ( EXPRESS ANSWER IN SLOPE–INTERCEPT FORM ) THEOREM Slope–Intercept Form of an Equation of a Line An equation of a line with slope m and y -intercept b is = + y mx b (3)
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