Question

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

Answer 1

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.