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Use the image to answer the question.

A coordinate plane shows a graph of an upward-sloping, solid, diagonal line, with shading extending from the line to the left. The line begins in quadrant 4 and ends in quadrant 1.

Which of the following points is a solution to the linear inequality 4x−y≤10 , as shown on the graph?

Option #1: (212,−12)

Option #2: (2,−3)

Option #3: (3,2)

(1 point)
The point in Option #
is a solution to the linear inequality

1 answer

To determine which point is a solution to the linear inequality \(4x - y \leq 10\), we need to substitute the coordinates of each option into the inequality and check if the resulting statement is true.

  1. Option #1: \((212, -12)\) \[ 4(212) - (-12) \leq 10 \ 848 + 12 \leq 10 \ 860 \leq 10 \quad \text{(false)} \]

  2. Option #2: \((2, -3)\) \[ 4(2) - (-3) \leq 10 \ 8 + 3 \leq 10 \ 11 \leq 10 \quad \text{(false)} \]

  3. Option #3: \((3, 2)\) \[ 4(3) - 2 \leq 10 \ 12 - 2 \leq 10 \ 10 \leq 10 \quad \text{(true)} \]

Therefore, the point in Option #3 \((3, 2)\) is a solution to the linear inequality \(4x - y \leq 10\).

So the answer is: The point in Option 3 is a solution to the linear inequality.