Section 3.3 The Slope of a Line 229 Notice from the graph that if we move right 4 units from the point (0, -2), we will be at the point (4, -2) since there is no movement up or down. 1e. Since we are given the graph of a line, we can find the slope by identifying two points on the graph and substituting their values in the slope formula. We can also find the ratio of the vertical change to the horizontal change. Method 1: Two points on the graph Method 2: To move from (0, 3) to (5, 0), are (5, 0) and (0, 3). So, we go down 3 units and right 5 units. m = y2 - y1 x2 - x1 m = 3 - 0 0 - 5 m = 3 -5 m=- 3 5 –2 x So, the slope is m = 6 vertical change horizontal change = -3 5 =- 3 5 Notice that as we examine the lines in Example 1, we find that • The line in 1a “goes up” from left to right or has positive slope. • The line in 1b “goes down” from left to right or has negative slope. • The line in 1c is “vertical” and has an undefined slope. • The line in 1d is “horizontal” and has a zero slope. So, we have four different possibilities for the slope of a line. x y Positive slope x y Negative slope x y Undefined slope x y Zero slope (0, –2) (4, –2) No movement up or down Right 4 units 2 –4 –2 2 4 –4 –6 x y 4 –2 y Down 3 Right 5
hendricks_beginning_algebra_1e_ch1_3
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