Explanation:
the point- slope format is
y - y1 = m(x - x1)
m is the slope, and (x1, y1) is a point on the line.
the slope is the ratio "y coordinate difference / x coordinate difference" when going from one point to another.
for the 2 given points we see
x changes by +3 (from -2 to +1).
y changes by +9 ) from -3 to +6).
so, the slope m is +9/+3 = 3.
the point-slope equation is then (by using the suggested point) :
y - 6 = 3(x - 1)
and from there we can get to the slope-intercept form by simply rearranging things.
the general slope-intercept form is
y = mx + b
again, m is the slope, and b is the y-intercept (the y value when x = 0).
y - 6 = 3x - 3
y = 3x + 3
so, the fourth answer option is correct.