# Product Of Slopes Of X,y Axes=0

• extreme_machinations
In summary, the conversation discussed the slopes of different lines, their product, and the concept of perpendicular lines. It also touched on the idea of infinity and its relationship with zero. The conversation ended with a disagreement about the use of the word "conjecture."
extreme_machinations
This Is Strange !

Slope Of The Line X= 0[y- Axis] Is =+1
Slope Of The Line Y=0 [x-axis] Is= 0
Product Of The Slopes = 0

Now Product Of Two Perpendicular Lines Should Be = - 1

It's funny how both the y-axis and the line y=x have the same gradient according to you

well ,
its even funnier how lack of reading skills can hamper a persons understanding .

if u pay attention sire ,u'll find that i said
that the line y=0 ,which you would agree is the x - axis and has a slope = 0

extreme_machinations said:
well ,
its even funnier how lack of reading skills can hamper a persons understanding .

if u pay attention sire ,u'll find that i said
that the line y=0 ,which you would agree is the x - axis and has a slope = 0
I don't disagree with you, but do you know what the gradient of the line x=0 (the y-axis) is?

If you work that out you will understand where you went wrong. Please don't be so offended I was just lightly trying to point out your mistake.

This reminds me of the "proof" that 1 = 2. The mistake involved dividing by zero or something. ;)

extreme_machinations said:
well ,
its even funnier how lack of reading skills can hamper a persons understanding .

if u pay attention sire ,u'll find that i said
that the line y=0 ,which you would agree is the x - axis and has a slope = 0

Good advice. You should take it yourself. Zurtex did not say anything about "the line y=0, which you would agree is the x-axis". He specifically referred to the "y-axis" and his point was that its slope is not 1!

The slope of the y-axis (x=0) is infinite. And, as we all know, infinity times zero equals negative 1. :)

oopsey !
tan 45 syndrome !
sorry for that ,

but i thought anything multiplied by 0 is = 0
infinity multiplied by zero being -1 is brand new information to me ,can anyone tell me how this so ??

extreme_machinations said:
oopsey !
tan 45 syndrome !
sorry for that ,

but i thought anything multiplied by 0 is = 0
infinity multiplied by zero being -1 is brand new information to me ,can anyone tell me how this so ??
Infinity multiplied by 0 is not -1, heck it doesn't even make sense. But what you can do is work out the limit of the 2 sides when multiplied by each other, which goes something like this:

$$\lim_{x \rightarrow \infty} -x \frac{1}{x} = -1$$

Now although it's true that:

$$\lim_{x \rightarrow \infty} -x = -\infty$$

And:

$$\lim_{x \rightarrow \infty} \frac{1}{x} = 0$$

It only makes sense to say:

$$\lim_{x \rightarrow \infty} f(x) g(x) = \left( \lim_{x \rightarrow \infty} f(x) \right) \left( \lim_{x \rightarrow \infty} g(x) \right)$$

If f(x) and g(x) have limits as x approaches infinity. And as we see above -x has no limit as x approaches infinity.

Consider the following two lines:

Line A: y = -nx
Line B: y = x/n

The gradients of these two lines are:

Because any two lines which are perpendicular have gradients which multiply to give -1, we see immediately that line A is perpendicular to line B, for any given value of n.

Now, consider what happens in the limit as n goes to infinity. For line B we have:

$$\lim_{n \rightarrow \infty} y = \lim_{n \rightarrow \infty} x/n = 0$$

So, line B becomes the line y = 0.

We can write line A as:

x = -y/n

Taking the limit as n goes to infinity, we see that this line becomes the line x = 0.

Since we have taken the same limit in both cases, the lines A and B have remained perpendicular, and their gradients must still multiply to give -1. What we have, n terms of the gradients, is:

$$\lim_{n \rightarrow \infty} (-n)(1/n) = \lim_{n \rightarrow \infty} -1 = -1$$

Anukriti C.
hey that's great conjecture !

thanks

extreme_machinations said:
hey that's great conjecture !

thanks

What "conjecture" are you talking about? I didn't see any conjecture in this.

I Was Just Using It In The General Sense ,not Strictly In The Mathematical Sense .

Please Ignore Whatever Does'nt Make Sense To You .

What general sense then? I thought I knew what "conjecture" meant, even in general- and I don't see how it applies. Enlighten me.

ok ,you win pal !
im not going to argue .
tell me what it was .

peace out ,

## 1) What does it mean for the product of slopes of x,y axes to equal 0?

When the product of slopes of x and y axes equals 0, it means that either the x-axis or the y-axis has a slope of 0. In other words, the line or plane is parallel to one of the axes, making the slope of that axis 0.

## 2) Can the product of slopes of x,y axes ever be greater than 0?

No, the product of slopes of x and y axes can never be greater than 0. This is because if one of the axes has a slope of 0, then the product will always be 0, regardless of the slope of the other axis.

## 3) How does the product of slopes of x,y axes relate to the slope of a line?

The product of slopes of x and y axes is related to the slope of a line by the fact that it is equal to the slope of the line. This is because the slope of a line is the ratio of the vertical change (change in y) to the horizontal change (change in x), and this can also be expressed as the product of the slopes of the x and y axes.

## 4) What is the significance of the product of slopes of x,y axes in mathematics?

The product of slopes of x and y axes is significant in mathematics because it helps to determine the orientation of a line or plane. It also helps to determine if a line or plane is parallel to one of the axes, as well as the slope of the line or plane.

## 5) How can the product of slopes of x,y axes be used in real-world applications?

The product of slopes of x and y axes can be used in real-world applications, such as engineering and physics, to determine the orientation and slope of objects and structures. It can also be used to calculate the angle of inclination of a line or plane, which is useful in fields like architecture and construction.

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