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<−12x−3 . Is the point (−1,4) part of the solution set? Enter 1 for yes or 2 for no.
(1 point)
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)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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).
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).
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