Which of the points are solution to the inequality? Check all that apply.
y < 2x + 3
A. (-3,3)
B. (-2,-2)
C. (-1,1)
D. (0,1)
E. (2,5)
We can sketch each point on the graph and find out if each point lies in the shaded zone. If so, it is a solution to the inequality, otherwise, it's not.
We see from the graph attached that
A is outside of the shaded area, so it is NOT a solution.
B is inside the shaded area, it is a solution.
C is on the boundary line. However, the boundary line is dotted, meaning only a strict inequality qualifies (i.e. equality does not count), so it is NOT a solution.
D is within the shaded area, so it is a solution.
E is within the shaded area, so it is a solution.
Alternate solution:
We can substitute the values of (x,y) into the inequality and see if the inequality is satisfied. If the evaluated values satisfy the inequality, then (x,y) used is a solution.
A. (-3,3) => 3<2(-3)+3=-3 since 3>-3, so (-3,3) is NOT a solution.
B. (-2,-2) => -2<2(-2)+3=-1 since -2<-1, so it (-2,-2) is a solution.
C. (-1,1) => 1<2(-1)+3=1 since 1=1 (and not <1), so (-1,1) is NOT a solution
D. (0,1) => 1<2(0)+3=3 since 1<3, (0,1) is a solution
E. (2,5) => 5<2(2)+3=7 since 5<7, (2,5) is a solution.
So we come to the same conclusions at the graphical method.