Question

Find the gradient of the following line with equation y=-3x-1

Answer 1

\[Gradient=\nabla=\frac{ \partial y }{ \partial x }i+\frac{ \partial y }{ \partial y }j+\frac{ \partial y }{ \partial z}k\]

Answer 2

that makes no sense to me what so ever

Answer 3

That is definitely the linear algebra definition, but in the simplest 1 dimensional case, the gradient is simply the slope

Answer 4

His answer is perfectly correct, it's the most general way, and includes a 3 dimensional space, but you're only dealing with 2 dimension, excuse me putting 1 dimension previously

Answer 5

He can be correct but that doesnt mean I follow .. I dont quite undertand what I am meant to do with the equation. My online class isnt making any sense what so ever.

Answer 6

So as i said, gradient is simply the slope, and slope is calculated by taking the derivative of your function with respect to x, meaning x is the variable, all other variables are considered constants\[gradient=\frac{ d }{ dx }\left[ -3x-1 \right]\]

Answer 7

where are you pulling d from ?

Answer 8

\[\frac{ d }{ dx }\]is another way of writing "take the derivative of this equation"'
i assume if you've learned what a derivative is, that you've probably seen it as\[y'=blah\]

Answer 9

no

Answer 10

never before, :/

Answer 11

Never before as in, you haven't learned what a derivative is? or you've never seen it as\[\frac{ d }{ dx }\]

Answer 12

i have learnt.

Answer 13

my module is that all over the place im not following a single thing

Answer 14

haven't

Answer 15

Well then, if you haven't learned what a derivative is yet, the only definition for what the gradient of something is, well that's the slope of the function, so if you recall the general equation of a line\[y=mx+b\]in this case, m is considered the slope, and yes, you include the negative with the m if the "mx" part happens to be "-mx"

Answer 16

so my equation y=-3x-1 -3 is m

Answer 17

Yup, that's correct, and then that is also the gradient of that function

Answer 18

and the gradient is the answer to \[\frac{ rise }{ run }\]

Answer 19

Yes, that is another definition of slope, as well as gradient in this case

Answer 20

okay so taking the y=mx-b -3 = \[\frac{ rise }{ run }\]

Answer 21

Yes, except that it's y=mx+b, it's +b not minus, the negative part would be the value that b would take, you don't take the negative of it, in general, it's y=mx+b

Answer 22

you can have b=-number is what i'm trying to say, so the negative would be located there, not in the general equation

Answer 23

oh yep
so what is the -1 for ? do i need to find x and y ?

Answer 24

-1 is your b, b=-1 which means that the graph goes through the point (0,-1) for sure, b is known as your y-intercept, it has no relevance when asked what the slope of a line is

Answer 25

ok so -1 is there just to confuse me.

Answer 26

in this question yes

Answer 27

so it can change in others ?

Answer 28

that -1 would only be relevant if you were asked to find the y-intercept of the graph, or to find the vertex of more complex graphs, like say the graph\[y=x^2\]which is another topic that you will learn eventually

Answer 29

okay. i think i got it :) thank you