Question

which line has a slope of \\(\frac{1}{6}\\)? options: line n, none of these, line q, line p. (image shows a coordinate grid with line n, line p, line q, line r)

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 \(\frac{1}{6}\) means for a run (change in \( x \)) of 6, the rise (change in \( y \)) is 1 (or smaller equivalent fractions, but we analyze the lines).

Step2: Analyze Line n

Line n is decreasing (negative slope), so its slope is negative, not \(\frac{1}{6}\).

Step3: Analyze Line p

Line p has a steeper positive slope (rise over run seems larger, e.g., if we take two points, the \( \frac{\Delta y}{\Delta x} \) is more than \(\frac{1}{6}\)).

Step4: Analyze Line q

Line q is a shallow positive slope. Let's check the grid: for a run of 6 units (horizontal change), the rise (vertical change) is 1 unit. So its slope is \(\frac{1}{6}\).

Step5: Analyze Line r

Line r is decreasing (negative slope), so its slope is negative, not \(\frac{1}{6}\).

Answer:

Line q