Question

Doesthepoint(3, 10)satisfytheinequality
y
>
–2
3
x
+ 2
?

Answer 1

To determine if the point (3, 10) satisfies the inequality \( y > -\frac{2}{3}x + 2 \), we will substitute \( x = 3 \) and \( y = 10 \) into the inequality.

1. **Calculate the right side of the inequality:**

\[
-\frac{2}{3}x + 2 = -\frac{2}{3}(3) + 2
\]
\[
= -2 + 2 = 0
\]

2. **Substituting the values into the inequality:**

Now we have to check if:

\[
10 > 0
\]

3. **Evaluate the inequality:**

Since \( 10 > 0 \) is true, the point (3, 10) does satisfy the inequality.

Therefore, the point (3, 10) does satisfy the inequality \( y > -\frac{2}{3}x + 2 \).