SECTION 1.5 Lines 35 Figures 52 and 53 illustrate the following facts: • When the slope of a line is positive, the line slants upward from left to right ( ) L . 1 • When the slope of a line is negative, the line slants downward from left to right ( ) L . 2 • When the slope is 0, the line is horizontal ( ) L . 3 • When the slope is undefined, the line is vertical ( ) L . 4 Figures 52 and 53 also illustrate that the closer the line is to the vertical position, the greater the magnitude of the slope. Thus, a line with slope 6 is steeper than a line whose slope is 3. Similarly, a line with slope −6 is steeper than a line with slope −3 since 6 3 . − > − Now Work PROBLEM 25 Figure 55 x y –2 10 (8, –2) (–2, 6) (3, 2) 6 –2 Run = 5 Run = –5 Rise = 4 Rise = –4 Figure 54 x y –2 10 Rise = 3 Run = 4 (7, 5) (3, 2) 5 6 Graphing a Line Given a Point and a Slope Draw a graph of the line that contains the point ( ) 3, 2 and has a slope of: (a) 3 4 (b) − 4 5 Solution EXAMPLE 2 (a) = Slope Rise Run . The slope 3 4 means that for every horizontal change (run) of 4 units to the right, there is a vertical change (rise) of 3 units. Start at the point ( ) 3, 2 and move 4 units to the right and 3 units up, arriving at the point ( ) 7, 5 . Drawing the line through the points ( ) 7, 5 and ( ) 3, 2 gives the graph. See Figure 54. (b) A slope of 4 5 4 5 Rise Run − = − = means that for every horizontal change of 5 units to the right, there is a corresponding vertical change of −4 units (a downward movement). Start at the point ( ) 3, 2 and move 5 units to the right and then 4 units down, arriving at the point ( ) − 8, 2 . Drawing the line through these points gives the graph. See Figure 55. 2 Graph Lines Given a Point and the Slope Alternatively, consider that 4 5 4 5 Rise Run − = − = so for every horizontal change of −5 units (a movement to the left), there is a corresponding vertical change of 4 units (upward). This approach leads to the point ( ) −2, 6 , which is also on the graph of the line in Figure 55.
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