Theslope of a lineis a measurement of the steepness and direction of a nonvertical line. When a line rises from left to right, the slope is a positive number. Figure 1(a) shows a line with a positive slope. When a line falls from left to right, the slope is a negative number. Figure 1(b) shows a line with a negative slope. Thex‐axis or any line parallel to thex‐axis has a slope of zero. Figure 1(c) shows a line whose slope is zero. They‐axis or any line parallel to they‐axis has no defined slope. Figure 1(d) shows a line with an undefined slope.
You are watching: Slope of a line parallel to x axis
Figure 1 Different possibilities for slope of a line.
Ifmrepresents the slope of a line andAandBare points with coordinates (xl,y1) and (x2,y2) respectively, then the slope of the line passing throughAandBis given by the following formula.
AandBcannot be points on a vertical line, sox1andx2cannot be equal to one another. lfx1=x2, then the line is vertical and the slope is undefined.
Example 1:Use Figureto find the slopes of linesa, b, c, andd.
Figure 2 Finding the slopes of specific lines.
a. (a) Lineapasses through the points (−7, 2) and (−3, 4).
b. (b) Linebpasses through the points (2, 4) and (6, −2).
c. (c) Linecis parallel to thex‐axis. Therefore,m= 0.
d. (d) Linedis parallel to they‐axis. Therefore, linedhas an undefined slope.
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Example 2:A line passes through (−5, 8) with a slope of 2/3. If another point on this line has coordinates (x, 12), findx.
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