Question

which number best represents the slope of the graphed line? a. -5 b. $-\frac{1}{5}$ c. $\frac{1}{5}$ d. 5

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Also, a line with a negative slope goes downward from left to right, and a steeper line has a slope with a larger absolute value.

Step2: Analyze the line's direction and steepness

The graphed line is decreasing (going down from left to right), so the slope should be negative. This eliminates options C (\(\frac{1}{5}\)) and D (5). Now, between A (-5) and B (\(-\frac{1}{5}\)), the line is quite steep. A slope of \(-\frac{1}{5}\) would be a gentle decrease, while a slope of -5 is a steep decrease. Looking at the graph, the line has a steep negative slope, so -5 is more appropriate.

Answer:

A. -5