Question

which line has a slope of \\(\frac{3}{4}\\)? \\(\bigcirc\\) line p \\(\bigcirc\\) line q \\(\bigcirc\\) line n \\(\bigcirc\\) none of these

Explanation:

Step1: Recall Slope Formula

The slope \( m \) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \), or "rise over run" (vertical change over horizontal change).

Step2: Analyze Each Line

• Line p: Observe two points on Line p. Count the rise (vertical change) and run (horizontal change). For a positive slope \( \frac{3}{4} \), rise should be 3, run 4. From the graph, Line p's points show a rise of 3 and run of 4 (e.g., moving from one green point to another: up 3, right 4), so slope \( \frac{3}{4} \).
• Line q: Has a small positive slope, less than \( \frac{3}{4} \) (run is larger relative to rise).
• Line n: Has a negative slope (going down from left to right).
• Line r: Has a negative slope (steeper negative).

Answer:

Line p