Which of the following points satisfies the inequality 2x + 3y ≤ -5?

Question

A.  (0, -1)

B. (0, 1)

C. (-4, 0)

D. (4, 0)

Answer 1

I plotted the equation rearranged in y=mx+b format as

y ≤ -2x/3 -5/3 and it is easy to see that only the point (-4,0) satisfies the inequality.

Answer 2

To check if a point satisfies the inequality, we can substitute each of the x and y values given in the choices to see which of them is correct.

A. 2(0) + 3(-1) =< -5

-3 =< -5

This is incorrect so the point does not satisfy the expression

B. 2(0) + 3(1) =< -5

3 =< -5

This one's also incorrect

C. 2(-4) + 3(0) =< -5

-5 =< -5

This one is true since they are equal, so this point satisfies the equation

D. 2(4) + 3(0) =< -5

11 =< -5

This one is incorrect

So the correct answer is C, (-4, 0)