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.

(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.