Explanation:
in what form do you need the equation ?
I assume it is the slope-intercept form :
y = ax + b
"a" being the slope of the line, "b" being the y-intercept of the line.
the slope of a line is the ratio
y-coordinate difference / x-coordinate difference
when going from one point on the line to another.
and the y-intercept (y-axis intercept, to be precise) is the y-value when x = 0.
so, starting with the slope, we go for example from (1, 6) to (6, 1) :
x changes by +5 (from 1 to 6).
y changes by -5 (from 6 to 1).
so, the slope is
-5/+5 = -1
so, we know, our equation looks like
y = -x + b
to get "b" we use one of the points, e.g. (1, 6) :
6 = -1 + b
b = 7
and our final equation is
y = -x + 7