The **slope of a line** is a measurement of the steepness and direction of a nonvertical line. When a line slants from lower left to upper right, the slope is a positive number. Item (a) in Figure 1 shows a line with a positive slope. When a line slants from upper left to lower right, the slope is a negative number (b). The *x‐*axis or any line parallel to the *x‐*axis has a slope of zero; that is, a horizontal line has a slope of zero (c). The *y*‐axis or any line parallel to the *y‐*axis has no defined slope; that is, a vertical line has an undefined slope (d).

Figure 1. Slopes of lines.

If *m* represents the slope of a line and *A* and *B* are points lying on that line with coordinates ( *x* _{1} *,y* _{1}) and ( *x* _{2} *,y* _{2}), respectively, then the slope of the line passing through *A* and *B* is given by the following formula.

Since *A* and *B* cannot be points on a vertical line, *x* _{1} and *x* _{2} cannot be equal to one another. If *x* _{1} *= x* _{2}, then the line is vertical, and the slope is undefined.

##### Example 1

Use Figure 2 to find the slopes of the lines *a, b, c*, and *d*.

Line *a* passes through the points (–7,2) and (–3,4).

Line *b* passes through the points (2,4) and (6,–2).

Line *c* is parallel to the *x*‐axis. Therefore,

*m* = 0

Line *d* is parallel to the *y*‐axis. Therefore, line *d* has an undefined slope.

##### Example 2

A line passes through (–5,8) with a slope of . If another point on this line has coordinates ( *x*,12), find *x*.