Use the image to answer the question.

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.

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 the \(x\) and \(y\) values of the point into the inequality.

1. Substitute \(-1\) for \(x\): \[ y < -\frac{1}{2}(-1) - 3 \] \[ y < \frac{1}{2} - 3 \] \[ y < \frac{1}{2} - \frac{6}{2} \] \[ y < -\frac{5}{2} \]

2. Now substitute \(4\) for \(y\): \[ 4 < -\frac{5}{2} \]

This statement is false. Therefore, the point \((-1, 4)\) is not part of the solution set for the inequality \(y < -\frac{1}{2}x - 3\).

The answer is 2 for no.