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messersmith_power_intermediate_algebra_1e_ch4_7_10

Definition The slope-intercept form of a line is y mx b, where m is the slope and (0, b) is the y-intercept. When an equation is in the form y mx b, we can quickly recognize the y-intercept and slope to graph the line. Remember that the b value is the y-coordinate of the y-intercept ordered pair. The y-intercept is always written as the ordered pair (0, b). EXAMPLE 6 Graph each line using its slope and y-intercept. a) y 3x 4 b) y 1 2 x c) 5x 3y 12 Solution a) Graph y 3x 4. Identify the slope, m, and y-intercept. y 3x 4 m 3,  y-intercept is (0, 4). Plot the y-intercept fi rst, then use the slope to locate another point on the line. Since the slope is 3, think of it as 3 1 . d change in y d change in x b) The equation y 1 2 x is the same as y 1 2 x 0. Identify the slope, m, and y-intercept. m 1 2 ,  y-intercept is (0, 0). Plot the y-intercept, then use the slope to locate another point on the line. Since 1 2 is equivalent to 1 2 , we can use 1 2 as the slope to locate yet another point on the line. c) Rewrite 5x 3y 12 in slope-intercept form, y mx b. 5x 3y 12 3y 5x 12 Add 5x to each side. y 5 3 x 4 Divide each side by 3. m 5 3 ,  y-intercept is (0, 4). We can interpret the slope of 5 3 as either 5 3 or 5 Right 1 unit 5 5 5 m 12 Right 2 Down 1 Up 1 5 5 5 5 3 y Up 3 units 5 (0, 4) y Left 2 5 m 1 y 5 Down 5 units 5 (0, 4) Right 3 units . Here we use (1, 1) 2 5 3 5 (3, 1) . Using either form will give us a point on the line. x x x www.mhhe.com/messersmith SECTION 4.2 Slope of a Line and Slope-Intercept Form 163


messersmith_power_intermediate_algebra_1e_ch4_7_10
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