Question

which linear inequality is represented by the graph?
○ $y \geq 2x + 3$
○ $y < 2x + 3$
○ $y > -2x + 3$
○ $y < -2x + 3$

Explanation:

Step1: Determine the slope and y-intercept

The line in the graph has a y-intercept at \( (0, 3) \) and passes through \( (1, 1) \). The slope \( m \) is calculated as \( \frac{1 - 3}{1 - 0} = -2 \). So the equation of the line is \( y = -2x + 3 \).

Step2: Check the inequality sign and line type

The line is dashed, so the inequality is strict (\( < \) or \( > \)). The shaded region is below the line, so we use \( y < -2x + 3 \).

Answer:

\( y < -2x + 3 \) (the fourth option: \( y < -2x + 3 \))