234 Chapter 3 Graphing Linear Equations in Two Variables Similarly, the slope can be written as m 5 2 To find a second point, start at the y-intercept and move up 5 units and to the left 2 units.Then draw the line through the two points (Figure 3-28). Skill Practice 6. Graph the equation by using the slope and the y-intercept. y 2x 3 Graphing a Line Using the Slope and y-Intercept Example 4 Graph the equation of the line y 4x by using the slope and y-intercept. Solution: The line can be written as y 4x 0. Therefore, we can plot the y-intercept at (0, 0).The slope can be written as m 4 1 m 4 The change in y is 4. The change in x is 1. To find a second point on the line, start at the y-intercept and move up 4 units and to the right 1 unit.Then draw the line through the two points (Figure 3-29). y Start here (0, 0) 1 2 3 4 5 54 321 5 4 3 2 1 1 2 3 4 5 Figure 3-29 x Skill Practice 7. Graph the equation by using the slope and the y-intercept. y 1 4 x 3. Determining Whether Two Lines Are Parallel, Perpendicular, or Neither The slope-intercept form provides a means to find the slope of a line by inspection. Recall that if the slopes of two lines are known, then we can compare the slopes to determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular. (Two distinct nonvertical lines are parallel if their slopes are equal. Two lines are perpendicular if the slope of one line is the opposite of the reciprocal of the slope of the other line.) Answers 6–7. 5 4 3 2 2 1 Figure 3-28 5 4 3 4 y 2x 3 2 1 y 543 21 1 2 3 4 5 1 2 3 4 5 x y 1 x y x 1 2 3 4 5 2 3 4 5 5432 1 (0, 3) Start here 1 5 The change in y is 5. The change in x is 2.
miller_beginning_intermediate_algebra_4e_ch1_3
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