The**slope that a line**is a measurement of the steepness and also direction of a nonvertical line. Once a line rises native left to right, the slope is a positive number. Number 1(a) mirrors a line v a confident slope. Once a line falls from left come right, the steep is a negative number. Figure 1(b) reflects a line through a an unfavorable slope. The*x*‐axis or any type of line parallel come the*x*‐axis has actually a steep of zero. Number 1(c) mirrors a line whose slope is zero. The*y*‐axis or any kind of line parallel to the*y*‐axis has actually no identified slope. Figure 1(d) reflects a line with an unknown slope.

You are watching: The slope of a line parallel to the vertical axis is:

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

If*m*represents the steep of a line and*A*and*B*are point out with collaborates (*x*l,*y*1) and (*x*2,*y*2) respectively, climate the slope of the heat passing through*A*and*B*is offered by the adhering to formula.

*A*and*B*cannot be points ~ above a vertical line, so*x*1and*x*2cannot be equal to one another. Lf*x*1=*x*2, climate the heat is vertical and the steep is undefined.

**Example 1:**Use Figureto discover the slopes that lines*a, b, c*, and*d.*

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

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

b. (b) Line*b*passes v the points (2, 4) and also (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 unknown slope.

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**Example 2:**A heat passes v (−5, 8) through a steep of 2/3. If another allude on this heat has works with (*x*, 12), find*x.*

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