How do u find gradients again?

• SleSSi
In summary, the conversation was about finding the gradient of a line and understanding its connection to the slope of the line. The gradient is calculated by taking the y-displacement divided by the x-displacement, and it represents how much y changes for every change in x. The gradient is also known as the slope of the line and is represented by the letter "m" in the equation y=mx+c. However, in the case of a vertical line, the gradient is undefined.
SleSSi
i need to find the gradient of the line y-3x=2 how do i do it again?

Put it in the form y = mx + c and m is the gradient.

What's the connection between the slope of the line & its gradient...?

Daniel.

hey,

{y-displacement}/{x-displacement} = gradient displacement is how much y changes and x changes from two points.

The gradient IS the slope of the line

Regards,

Ben

Last edited by a moderator:
Rise over Run - is how I remember it.

Wait, is this gradient the same gradient as in gradient of a vector field or does it mean gradient like slope of the line?

whozum said:
Wait, is this gradient the same gradient as in gradient of a vector field or does it mean gradient like slope of the line?

Slope of line - y=mx +c

Regards,

Ben

The original question was about y- 3x= 2, a real valued linear function of a single real variable. I'm afraid all that talk about "vectors" and even "derivatives" will just confuse the original poster.

Slessi: solve for y. In this example, solving for y gives y= 3x+ 2 so the gradient (slope) is 3. (Almost) any linear equation can be solved for y in the form y= mx+ b and the gradient is the number m.

(I say "(Almost)" because a vertical straight line, like x= 1, cannot be put in that form: it has NO gradient.

HallsofIvy said:
(I say "(Almost)" because a vertical straight line, like x= 1, cannot be put in that form: it has NO gradient.

I was just staring at this statement whilst drinking tea and began to think, there is a gradient because gradient is [y-displacement]/[x-displacement] and in this case, 0/change in x. Change in x is always a non-zero integer value and therefore the gradient is 0/non-zero integer = 0. Looking at the graph, this fits, the gradient looks to be 0.

However, if the graph is of y=1 ,then the equation becomes: [change in y]/0. Change in y is always a non-zero integer value and therefore the gradient is non-zero integer/0 which is mathematically undefined. However, if one looks at the graph in a topolgical sense (Pemrose is my source on the idea of topolgy), then the gradient looks to be -infinity or +infinity. And this leads one to consider what result dividing by 0 gives.

Anyway, those are just my thoughts,

Regards,

Ben

BenGoodchild said:
[y-displacement]/[x-displacement]
Yes, that's exactly right.
and in this case, 0/change in x.
No, that's exactly wrong. The equation in question is x= 1. x is always 1: x doesn't change, y can be anything: the equation is change in y/0.
. Change in x is always a non-zero integer value
Where in the world did you get that idea? If x= 1 the change is 0! x= 1 means exactly that: x is always 1, not the "change" in x!
However, if the graph is of y=1 ,then the equation becomes: [change in y]/0.
Same error: if y= 1 then y does not chage: the slope is 0/change in x= 0.

Hi, I commented on x=1 instead of y=1 and visa versa - please reread the post in its now corrected form (below) and give your throughts.

I was just staring at this statement whilst drinking tea and began to think, there is a gradient because gradient is [y-displacement]/[x-displacement] and in the case of y=1, 0/change in x. Change in x is always a non-zero integer value and therefore the gradient is 0/non-zero integer = 0. Looking at the graph, this fits, the gradient looks to be 0.

However, if the graph is of x=1 ,then the equation becomes: [change in y]/0. Change in y is always a non-zero integer value and therefore the gradient is non-zero integer/0 which is mathematically undefined. However, if one looks at the graph in a topolgical sense (Pemrose is my source on the idea of topolgy), then the gradient looks to be -infinity or +infinity. And this leads one to consider what result dividing by 0 gives.

-Ben

1. What is a gradient in science?

A gradient in science refers to the change in a variable over a certain distance. It can also be thought of as the slope or steepness of a graph.

2. How do you calculate a gradient?

To calculate a gradient, you need to find the change in the dependent variable (y) divided by the change in the independent variable (x). This is also known as rise over run or the slope formula.

3. Why is finding gradients important in science?

Finding gradients is important in science because it allows us to analyze and understand changes in variables over a certain distance or time. It can also help us make predictions and draw conclusions from data.

4. What are some real-world applications of gradients?

Gradients are used in various fields such as physics, engineering, and economics. Some examples of real-world applications include calculating the rate of change in temperature, determining the slope of a road or hill, and analyzing the growth rate of a population.

5. Can you provide an example of finding gradients in a graph?

Sure, let's say we have a distance-time graph for a car traveling at a constant speed. The gradient of this graph would represent the car's velocity, which is the change in distance over the change in time. So, if the gradient is steeper, it means the car is traveling at a faster speed.

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