Section 2.3 Equations of a Line 159 Graphing a Line Using the Slope and y-Intercept 34 Example 2 Graph the equation using the slope and y-intercept. Solution: First plot the y-intercept (0, 1).The slope can be written as m 3 4 m 34 y x 1 The change in y is 3. The change in x is 4. To find a second point on the line, start at the y-intercept and move down 3 units and to the right 4 units. Then draw the line through the two points (Figure 2-23). Similarly, the slope can be written as m 3 4 The change in y is 3. The change in x is 4. y 5 4 3 2 1 5432 1 1 2 3 4 5 1 2 3 4 To find a second point on the line, start at the y-intercept and move up 3 units and to the left 4 units. Then draw the line through the two points (see Figure 2-23). Skill Practice 2. Graph the equation using the slope and y-intercept. y 15 x 2 As we have seen earlier, two lines are parallel if they have the same slope and different y-intercepts.Two lines are perpendicular if the slope of one line is the opposite of the reciprocal of the slope of the other line. Otherwise, the lines are neither parallel nor perpendicular. Determining if Two Lines Are Parallel, Perpendicular, or Neither Example 3 Given the equations for two lines, L1 and L2, determine if the lines are parallel, perpendicular, or neither. a. b. c. L1: y 2x 7 L1: 2y 3x 2 L1: x y 6 L2: y 2x 1 L2: 4x 6y 12 L2: y 6 Solution: a. The equations are written in slope-intercept form. The slope is and the y-intercept is 10, 72. The slope is and the y-intercept is L1: y 2x 7 2 L2: y 2x 1 2 10, 12. Because the slopes are the same and the y-intercepts are different, the lines are parallel. x Start at y-intercept (0, 1) up 3 down 3 left 4 right 4 y x 1 34 5 Figure 2-23 Answer 2. 5 4 3 2 1 543 1 2 3 4 5 21 1 2 3 4 5 x y y x 2 1 5
miller_intermediate_algebra_4e_ch1_3
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