Explanation:
in what form (or format) do you need that equation ?
there are e.g. the slope-intercept form and the point-slope forms.
y = ax + b
is the slope intercept form ("a" is the slope, "b" is the y-intercept).
y - y1 = a(x - x1)
is the point-slope form ("a" is again the slope, x1,y1 are the coordinates of one point on the line).
they have the slope in common.
the slope of a line is the ratio
y coordinate difference / x coordinate difference
when gong from one point on the line to another.
we are given 2 points, so the point-slope form is the easiest to start with.
first the slope :
when going from (2, 7) to (1, 5)
x changes by -1 (from 2 to 1).
y changes by -2 (from 7 to 5).
the slope "a" is -2/-1 = 2.
and then I pick the point (1, 5), simply because it has the smaller numbers :
y - 5 = 2(x - 1)
that's the point-slope form.
to get the slope-intercept form, we only need make a simple transformation :
y - 5 = 2(x - 1) = 2x - 2
y = 2x + 3
that's it.