More Maths...yay

So I’m doing my maths homework and I came up against this:
a = (4,-1) b = (2,3)

(i) Find the slope of ab.

My only problem is the formula for finding the slope of a line is y = mx + c which clearly uses only one x and one y coordinate…so what do I do?

Ab is the line btw, not a multiplied by thingy.

y2-y1

x2-x1

a = (x1, y1) = (4, -1)
b = (x2, y2) = (2, 3)

m = (y1 - y2)/(x1-x2) = (-1 - 3)/(4 - 2) = (-4)/(2) = -2

y = -2x + b

Subbing the first point for y and x…

-1 = -2(4) + b
-1 = -8 + b
7 = b

y = -2x + 7

Also, either point could be (x1, y1) or (x2, y2). It only matters that you keep the order right ((y1 - y2)/(x1 - x2) instead of (x2 - x1).

if it’s only asking for the slope then you don’t even have to worry about the formula y=mx+b.

Why did I forget this >.>

Thanks guys.

I like to solve problems like this one this way:

If you add a third point, c = (2, -1), and use it to form a triangle with the other two ones, you’ll notice that the slope of ab equals tg (180º - â).

Maybe some people won’t see the character after 180º right, it’s an ‘a’ with a ^ on top of it. Also, I put the 180º there because the line is decreasing. If it weren’t, it’d be tg â.

From what I recall, this solution is the very definition of ‘slope’. The only reason I’m not 100% sure to say it is due to me not knowing math terminology in English so well, so please correct me if I made any mistakes.

wouldn’t that make it more difficult?

Difficulty is in the eyes of the beholder. There are people (me included) who find it a lot easier to do it the way I posted, because once you get the hang of it you can solve that problem in no time. See, when I looked at it, I pictured the triangle in my mind (I’m so used to it, it comes as an instinct already) and just thought “it’s 2 / [20^(1/2)]”. Took me a few seconds. After taking more time to elaborate we get {1 / [5^(1/2)]}.

There are many people who find the whe other way easier. If you remember the formula provided by Nightblade, you can solve most problems even faster. But I have a hard time memorizing formulas. I find it easier memorizing the definitions and making my way through them. In this case, the definition for slope of a line (if slope is what I’m thinking it is) is the tangent of the angle between the X axis and the right side of the line in question. And the triangle I cite has its hipotenusa over that line.

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