Question

What is the slope of any line perpendicular to the line passing through `(-2,7)` and `(-2,3)`?

Answer 1

`y=0` graph{y=0x [-9.83, 10.17, -4.96, 5.04]}

Explanation:

I'll be using slope-intercept form, `y=mx+b`, for this.

A perpendicular line is a line with a slope that is both the inverse and the reciprocal of the original slope. For example, `y=2/3` is perpendicular to `y=(-3/2)`. It does not matter what the y-intercept `b` is in this situation, the slope is what's important.

To find the slope, use the rise-over-run formula of `(y_2-y_1)/(x_2-x_1)`

`(3-7)/((-2)-(-2)) rArr (-4)/(0)`

This will be a special case. Since dividing by 0 is undefined, this makes your slope undefined. Contrary to the rules explained above, which should work for all other questions, your slope in this case is a perfectly horizontal line, as undefined is perfectly vertical.

A horizontal line is called a slope of zero. As you'll see, the name is quite fitting, because your answer is:

`y=0`