Question

Use the image to answer the question.

A dashed line with a negative slope is plotted on a 4-quadrant coordinate plane. The area below the line is shaded. A labeled coordinate point is plotted in the area above the line.

The graph shows the inequality y<−1/2x−3
. Is the point (−1,4)
part of the solution set? Enter 1 for yes or 2 for no.

(1 point)

Answer 1

To determine if the point \((-1,4)\) is part of the solution set for the inequality \(y < -\frac{1}{2}x - 3\), we can substitute \(x = -1\) and \(y = 4\) into the equation.

First, calculate \(-\frac{1}{2}(-1) - 3\):

\[
-\frac{1}{2}(-1) = \frac{1}{2}
\]

\[
\frac{1}{2} - 3 = \frac{1}{2} - \frac{6}{2} = -\frac{5}{2}
\]

So the equation becomes:

\[
y < -\frac{5}{2}
\]

Now, we check if \(y = 4\) satisfies this inequality:

\[
4 < -\frac{5}{2}
\]

This statement is false because \(4\) is greater than \(-\frac{5}{2}\).

Thus, the point \((-1, 4)\) is not part of the solution set of the inequality.

The answer is \(2\) for no.