Question

which line has a slope of -6? line b none of these line c line d

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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \). A slope of \(-6\) means a steep negative slope (large magnitude of vertical change over horizontal change).

Step2: Analyze Line Slopes

• Line a: Shallow positive slope (small \( |m| \)), not \(-6\).
• Line b: Shallow negative or positive? Wait, Line b's direction? Wait, looking at the graph, Line d is the steepest negative line. Let's check coordinates. Suppose Line d has points: let's take two points on Line d. From the graph, if we move 1 unit right (Δx = 1), how much does y change? A slope of -6 means Δy = -6 when Δx = 1. Line d is very steep, so its slope is -6 (steeper than Line c, which has a smaller negative slope magnitude). Line c: less steep (smaller |m|) than -6. So Line d has slope -6.

Answer:

Line d