To determine which of the following options is a solution to the inequality [tex]\( y < \frac{2}{3} x + 2 \)[/tex], we can check different points and see if they satisfy the inequality.
Let's analyze the point (0, 0):
1. Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 0 \)[/tex] into the inequality:
[tex]\[
y < \frac{2}{3} x + 2
\][/tex]
2. This becomes:
[tex]\[
0 < \frac{2}{3} \cdot 0 + 2
\][/tex]
[tex]\[
0 < 0 + 2
\][/tex]
[tex]\[
0 < 2
\][/tex]
The inequality [tex]\( 0 < 2 \)[/tex] is true, which means the point (0, 0) satisfies the inequality:
Therefore, the point [tex]\( (0,0) \)[/tex] is a solution to the inequality [tex]\( y < \frac{2}{3} x + 2 \)[/tex].
