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<−12x−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 \( y < -12x - 3 \), we can substitute \( x = -1 \) and \( y = 4 \) into the inequality and check if it holds true.

First, substitute \( x = -1 \) into the equation \( y = -12x - 3 \):

\[ y = -12(-1) - 3 \] \[ y = 12 - 3 \] \[ y = 9 \]

Now we compare \( y = 4 \) with \( y < 9 \).

Since \( 4 < 9 \) is true, it means that the point (−1, 4) satisfies the inequality \( y < -12x - 3 \).

Therefore, the point is part of the solution set.

The answer is 1 (for yes).