The **slope of a line** is 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. The *x*‐axis or any line parallel to the *x*‐axis has a slope of zero. Figure 1(c) shows a line whose slope is zero. The *y*‐axis or any line parallel to the *y*‐axis has no defined slope. Figure 1(d) shows a line with an undefined slope.

**Figure 1 **Different possibilities for slope of a line.

If *m* represents the slope of a line and *A* and *B* are points with coordinates ( *x* _{l}, *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.

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

**Example 1:** Use Figure to find the slopes of lines *a, b, c*, and *d.*

**Figure 2 ***Finding the slopes of specific lines.*

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

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

c. (c) Line *c* is parallel to the *x*‐axis. Therefore, *m* = 0.

d. (d) 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 2/3. If another point on this line has coordinates ( *x*, 12), find *x.*