b) Let (x1, y1) (3, 4) and (x2, y2) (3, 1). m y2 y1 x2 x1 1 4 3 (3) 5 0 undefined We say that the slope is undefi ned. Plotting these points gives us a vertical line. Each point on the line has an x-coordinate of 3, so x2 x1 always equals zero. The slope of every vertical line is undefi ned. Remember that if the denominator of a fraction is 0 it is said to be undefined. We cannot define a vertical line as going up or down, and therefore we say its slope is undefined. YOU TRY 3 Find the slope of the line containing each pair of points. a) (5, 8) and (2, 8) b) (4, 6) and (4, 1) Property Slopes of Horizontal and Vertical Lines The slope of a horizontal line, y b, is zero. The slope of a vertical line, x a, is undefi ned. (a and b are constants.) 5 Use Slope and One Point on a Line to Graph the Line We have seen how we can fi nd the slope of a line given two points on the line. Now, we will see how we can use the slope and one point on the line to graph the line. EXAMPLE 5 Graph the line containing the point a) (2, 5) with a slope of 7 2 5 (3, 4) 5 5 5 (3, 1) . b) (0, 4) with a slope of 3. Solution a) Plot the point (2, 5). Use the slope to fi nd another point on the line. m 7 2 change in y change in x To get from the point (2, 5) to another point on the line, move up 7 units in the y-direction and right 2 units in the x-direction. Plot this point, and draw a line through the two points. x y Slope is undefined x y 5 Right 2 units 5 5 Up 7 units 5 (2, 5) www.mhhe.com/messersmith SECTION 4.2 Slope of a Line and Slope-Intercept Form 161
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