Explanation:
in what form do you need the equation ?
I assume the most usual one : the slope-intercept form
y = ax + b
"a" being the slope, "b" being the y-intercept (the y-value when x=0, so, where the line intercepts the y-axis).
the slope is the ratio
y coordinate difference / x coordinate difference
when going from one point on the line to another.
the direction does not matter, as long as we use the same for the x- and the y-coordinates.
so, let's go from (4, -3) to (2, -4).
x changes by -2, from 4 to 2.
y changes by -1, from -3 to -4.
therefore the slope (a) is -1/-2 = ½.
that means we know the first part of the equation :
y = ½ x + b
we get "b" by using one of the 2 given points for x and y. I simply pick the first one (4, -3) :
-3 = ½×4 + b = 2 + b
-5 = b
the equation is (you pick the format your teacher prefers) :
y = ½ x - 5 = x/2 - 5