If the slope is negative is the rise OR the run negative?

Answer 1

Tenbong and Northstar are both correct. Really, its a matter of perspective. As ironic, or even contradictory, as it may seem, I am forced to acknowledge the validity of both.

For the most part, we humans with our human minds tend the view number lines in an increasing fashion. That is why the left half of the x-axis is negative, after all... why do you think we arbitrarily default to that setting?

Chicken and the egg, right. Which came first, our perception that left-to-right equates to negative-to-positive, and that is why we graph the way we do? Or did the graphing standard instill the way of thinking?

The way I see it, when viewing an arbitrary graph, run will increase from a left to right direction... that is by definition, after all. Run is an increase over the x-axis dimension.

Therefore, our perception of rise is based on the trend on th y-axis coordinates effected by the function on the increasing x-axis coordinates.

Although, within any particular function... and even I do this often by habit... I will pick a point on a function as a reference point. Say, the vertex of a parabola. Right of the vertex in an upward-opening parabola, I say that rise increases and run increases.... while to the left of the vertex I would say that rise increases while run decreases.

But, like I said, its a matter of perspective. From the far far left... negative infinity... from left to right on the graphing paper, itself... run will continuously increase from left to right. Run decreases until the vertex and increases after the vertex.

What about a line with a slope of 1? Is that a rise of 1 over a run of 1 from left to right? Or is it viewed from right to left, a run of -1 and a rise of -1? This is what Northstar is talking about. If rise and run have the same sign, slope will be positive from a left to right direction.

On the other hand, if the function increases from left to right then the slope could be negative if the x-axis was more negative on the right.

Its not just a matter of perception of the qualities of the function, itself... but the context of the graphing standard also plays a part in this perception.

Answer 2

It really doesn't matter. If the slope is negative then the rise and run have opposite signs. If the slope is positive then the sign of the rise and run are the same.

Answer 3

It depends which way you subtract your points to find the slope.

For example, suppose that (1, 0) and (0, 1) are two points on a line. If we subtract the values in the second point from the first, we get

Rise = -1, Run = 1.

If we subtract the values in the first point from the second, we get

Rise = 1, Run = -1.

So it could be either the rise or the run that's negative. It just depends which order you subtract your points in. (Of course, if both are positive or both are negative, you'll get a positive slope instead.)

Answer 4

if the slope is negative, then the rise is negative, not the run. that's because the slope is the rise. :)

when you get a slope that's a negative fraction, the same thing applies: the rise is negative, the run is positive.

Answer 5

if the slope is negative, when you look at the graph from left to right, we see a a drop/descent rather than a rise/ascent.

the "run" is always from left to right (x increases), so to answer your question the rise is negative when the slope is negative