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: (2 1/2,−1/2)

Option #2: (2,−3)

Option #3: (3,2)

(1 point)
The point in Option #
is a solution to the linear inequality 4x−y≤10
.

Answer 1

To determine which point is a solution to the linear inequality \( 4x - y \leq 10 \), we need to test each of the options in the inequality.

1. **Option #1: \( (2.5, -0.5) \)**
Substitute \( x = 2.5 \) and \( y = -0.5 \) into the inequality:
\[
4(2.5) - (-0.5) \leq 10
\]
\[
10 + 0.5 \leq 10
\]
\[
10.5 \leq 10 \quad (\text{False})
\]

2. **Option #2: \( (2, -3) \)**
Substitute \( x = 2 \) and \( y = -3 \) into the inequality:
\[
4(2) - (-3) \leq 10
\]
\[
8 + 3 \leq 10
\]
\[
11 \leq 10 \quad (\text{False})
\]

3. **Option #3: \( (3, 2) \)**
Substitute \( x = 3 \) and \( y = 2 \) into the inequality:
\[
4(3) - 2 \leq 10
\]
\[
12 - 2 \leq 10
\]
\[
10 \leq 10 \quad (\text{True})
\]

Based on the evaluations, the point that satisfies the inequality \( 4x - y \leq 10 \) is:

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