Explanation:
the slope-intercept form always looks like
y = ax + b
with "a" being the slope, "b" being the y-intercept (the y- value when x = 0).
the slope is the ratio
y coordinate difference / x coordinate difference
when going from one point on the line to another.
we got 2 points
(-5, -4) and (1, 2)
x changes by +6 (from -5 to 1).
y changes by +6 (from -4 to 2).
so, the slope (a) is +6/+6 = 1.
we get "b" by using the coordinates of one of the given points (I pick (1, 2)) in the "half-finished" equation :
2 = 1×1 + b = 1 + b
b = 1
so, our equation is
y = x + 1