Question

line l is shown below. right triangles abc and def are drawn to measure the slope of the line. complete the parts below. (a) find the run, rise, and slope given by triangle abc.

Explanation:

Step1: Identify run and rise for triangle ABC

Run is horizontal change, rise is vertical change. From the graph, for triangle ABC, if we assume the coordinates of \(A\) and \(C\), the run is the horizontal distance between \(A\) and \(C\). Counting the grid - squares, the run \(= 4\). The rise is the vertical distance between \(B\) and \(C\). Counting the grid - squares, the rise \(= 8\).

Step2: Calculate the slope

The slope \(m\) of a line is given by the formula \(m=\frac{\text{rise}}{\text{run}}\). Substituting the values of rise \( = 8\) and run \(=4\) into the formula, we get \(m = \frac{8}{4}=2\).

Answer:

Run: 4, Rise: 8, Slope: 2