Question

which line has a slope of \\(\frac{1}{4}\\)? \\(\bigcirc\\) line t \\(\bigcirc\\) none of these \\(\bigcirc\\) line s \\(\bigcirc\\) line v

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \), or for a line on a grid, \( m=\frac{\text{rise}}{\text{run}} \) (change in \( y \) over change in \( x \)).

Step2: Analyze Line t

For Line t (red line), pick two points. Let's take two red dots. Suppose we move from one dot to the next: the rise (change in \( y \)) is \( 1 \) (up 1 unit) and the run (change in \( x \)) is \( 4 \) (right 4 units). So slope \( m=\frac{1}{4} \).

Step3: Analyze other lines (optional check)

• Line s: The rise over run would be steeper (e.g., rise 1, run 1? No, but visually, its slope is greater than \( \frac{1}{4} \)).
• Line v: It's a vertical line? No, it's a steep line, slope is undefined or very large (vertical/near - vertical, slope is infinite or large negative/positive, not \( \frac{1}{4} \)).
• Line u: It's a steep negative slope line, so slope is negative, not \( \frac{1}{4} \).

Answer:

Line t