Question

which line has a slope of -8? line h line g none of these line f

Explanation:

Step1: Recall Slope Formula

The slope \( m \) of a line is calculated as \( m=\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1,y_1) \) and \( (x_2,y_2) \) are two points on the line. A slope of \(-8\) means a steep negative slope (large negative change in \( y \) for small change in \( x \)).

Step2: Analyze Line Slopes

• Line e: Positive slope (rising from left to right), so slope \(>0\), not \(-8\).
• Line f: Shallow positive slope (small \( \frac{\Delta y}{\Delta x} \)), slope \(>0\) and small, not \(-8\).
• Line h: Appears to have a steep negative slope. Visually, for a small \( \Delta x \) (e.g., \( \Delta x = 1 \)), \( \Delta y \) is large negative (consistent with slope \(-8\)’s steepness). Other lines don’t match the steep negative slope of \(-8\).

Answer:

Line h