Question

Doesthepoint(–8, –8)satisfytheinequality
y ≥ –1/2x − 10?

Answer 1

To determine whether the point (-8, -8) satisfies the inequality \( y \geq -\frac{1}{2}x - 10 \), we can substitute \( x = -8 \) and \( y = -8 \) into the inequality.

First, substitute \( x = -8 \) into the right side of the inequality:

\[
y \geq -\frac{1}{2}(-8) - 10
\]

Calculating the right side:

\[
-\frac{1}{2}(-8) = 4
\]
\[
4 - 10 = -6
\]

Now the inequality becomes:

\[
y \geq -6
\]

Since we have \( y = -8 \), we replace it in the inequality:

\[
-8 \geq -6
\]

This statement is false. Therefore, the point (-8, -8) does not satisfy the inequality \( y \geq -\frac{1}{2}x - 10 \).