Step-by-step explanation:
the second option.
you see that the steeper line has a slope of -3 (when x increases by 1 grid point, y decreases by 3 grid points, that makes the slope ratio of y/x = -3/1 = -3).
the slope is always the factor of x in an equation of
y = ax + b
the only equation provided in the answer options with slope -3 is
-y <= 3x + 4
because when we transform this into the general firm above, we need to multiply both sides by -1 (which flips the inequality symbol, by the way) :
y >= -3x - 4
there you have it. no other equation here can be transformed into this.
as a control we also look at the second equation :
-3x + 3y <= -9
3y <= 3x - 9
y <= x - 3
this has a slope of 1 (so, x and y both increase by the same amount), and the y-inteecept is -3 (the y value when x = 0). that also fits the graph.
so, it is all correct.
