Question
In the graph for the solution set of the inequality 4x - 3y > 6, identify the coordinate that is a solution. (1 point)
O (0, -2)
O (2,0)
O (0,2)
O (-2, 0)
O (0, -2)
O (2,0)
O (0,2)
O (-2, 0)
Answers
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Answered by
GPT-4o mini
To determine which of the given points is a solution to the inequality \(4x - 3y > 6\), we can substitute the coordinates of each point into the inequality and check if it holds true.
1. For the point \((0, -2)\):
\[
4(0) - 3(-2) = 0 + 6 = 6
\]
Since \(6 > 6\) is false, this point is not a solution.
2. For the point \((2, 0)\):
\[
4(2) - 3(0) = 8 - 0 = 8
\]
Since \(8 > 6\) is true, this point is a solution.
3. For the point \((0, 2)\):
\[
4(0) - 3(2) = 0 - 6 = -6
\]
Since \(-6 > 6\) is false, this point is not a solution.
4. For the point \((-2, 0)\):
\[
4(-2) - 3(0) = -8 - 0 = -8
\]
Since \(-8 > 6\) is false, this point is not a solution.
The only point that satisfies the inequality \(4x - 3y > 6\) is \((2, 0)\). Thus, the correct answer is:
**O (2, 0)**.
1. For the point \((0, -2)\):
\[
4(0) - 3(-2) = 0 + 6 = 6
\]
Since \(6 > 6\) is false, this point is not a solution.
2. For the point \((2, 0)\):
\[
4(2) - 3(0) = 8 - 0 = 8
\]
Since \(8 > 6\) is true, this point is a solution.
3. For the point \((0, 2)\):
\[
4(0) - 3(2) = 0 - 6 = -6
\]
Since \(-6 > 6\) is false, this point is not a solution.
4. For the point \((-2, 0)\):
\[
4(-2) - 3(0) = -8 - 0 = -8
\]
Since \(-8 > 6\) is false, this point is not a solution.
The only point that satisfies the inequality \(4x - 3y > 6\) is \((2, 0)\). Thus, the correct answer is:
**O (2, 0)**.
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