Question

slope = -5/2

Explanation:

Step1: Recall Slope Formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). A negative slope means the line decreases from left to right, and \( |m|=\frac{5}{2}=2.5 \), so the line should be steep (large absolute slope) and decreasing.

Step2: Analyze Each Graph

• Blue Graph: Check two points. Let's say the line passes through \((0, 3)\) and \((2, -2)\). Then \( m=\frac{-2 - 3}{2 - 0}=\frac{-5}{2}=- \frac{5}{2} \). This matches the slope.
• Red Graph: The line is increasing (positive slope), so eliminate.
• Orange Graph: Let's check points. If it passes through \((0, 3)\) and \((1, -2)\), \( m=\frac{-2 - 3}{1 - 0}=-5 \), not \(-\frac{5}{2}\).
• Green Graph: The slope is very small (close to 0, since it's almost horizontal), so eliminate.

Answer:

The graph in the Blue box