Question

Describe what is meant by the slope of a nonvertical line. Explain how your description relates to the definition of slope

Answer 1

The slope of a nonvertical line is-

• In a coordinate plane, the slope of a nonvertical line is defined as follows:

Let P1(x1, y1) and P2(x2, y2) Any two locations on the line can be.

Then there's the line's slope =$\frac{y2 - y1}{x2 -x1}$

        =Change in y/change in x=$\frac{rise}{run}$

There is no slope on a vertical line.

• There is only one slope on a nonvertical line. That is, it doesn't matter which pair of points on the line you use to compute the slope; the result will always be the same.

Reason: The right-hand triangles are comparable, so:

Rise/run = rise’/run’

If the run is positive, the "rise" can be positive, negative, or zero for finding (or estimating) slopes. In addition, if you take the run to be 1, the increase is really the line's slope.

• The slope of non vertical parallel lines is the same. Nonvertical lines having the same slope, on the other hand, are parallel.

• If and only if, the slopes of two nonvertical lines are negative reciprocals of one another, they are perpendicular.