Given that (4, 5) and (-8, -4) are two points on a line, find the equation of the line and write your final answer in slope–intercept

That's the way math works sometimes......If you don't see it....you don't see it......then.......when you do see it....you wonder why you didn't see it in the first place  !!!!  LOL!!!

The form we want is:

$${\mathtt{y}} = {\mathtt{mx}}{\mathtt{\,\small\textbf+\,}}{\mathtt{b}}$$

m = Δy/Δx

Δy = $$y_{2}$$-$$y_{1}$$

Δx = $$x_{2}$$-$$x_{1}$$

$${\mathtt{m}} = {\frac{\left({\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,-\,}}{\mathtt{5}}\right)}{\left({\mathtt{\,-\,}}{\mathtt{8}}{\mathtt{\,-\,}}{\mathtt{4}}\right)}}$$ 

So m = 0.75.

$${\mathtt{b}} = {\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{mx}}$$

We take one of the points and insert its coordinates into y and x.

b = 5 - 0.75 * 4 = 17

So the form is $${\mathtt{y}} = {\mathtt{0.75}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{17}}$$

Thanks but I am still a bit confused about this one

We'll use y = mx + b

First, we need to find the slope, (m)........this is defined as ......the change in y /  change in x

Look at  (4, 5) and (-8, -4)

Note that, from the first point to the second, y changes by -9

And x changes by  -12

So.....the slope is    -9 / -12  = -3 / -4   = 3/4  = "m"

Now using either one of the points - i'll use the first one -we can substitute for y, m and x in y = mx + b to find "b"....so we have

5= (3/4)(4) + b  simplify

5= 3 + b    subtract 3 from both sides

b = 2

So our equation is

y = (3/4)x + 2

Check to see that the second point "works" in this equation.....just fill in for "x" and "y'

Does that help??

Nope, still lost :/

What's giving you trouble??  calculating the slope??.....or simplifying the equation??......something else??

Wait!! I got it now! Just needed to sink it in :) Thanks!

Hah. You're really really great at maths. Seriously wish I was this great too lol

I'm not that great.....more just lucky.....!!!!