Question

on the graph of a line, you can use a rate triangle, drawn between any 2 points, to determine the slope of the line.
rate of change (or slope) = \\( \frac { height } { base } \\)
m (or rate of change) = \\( \frac { height \to rise } { base \to run } \\)
rate of change = \\( \frac { rise (or fall) } { run } \\)

Explanation:

Step1: Understand the concept of slope

The slope \(m\) of a line is calculated using the formula \(m=\frac{\text{rise}}{\text{run}}\). The "rise" is the vertical change (height) between two points on the line, and the "run" is the horizontal change (base) between those two points.

Step2: Visualize with the rate triangle

In the given rate - triangle (a right - triangle drawn between two points on the line), the vertical side of the triangle represents the "rise" (positive if going up, negative if going down) and the horizontal side represents the "run" (always positive when moving from left to right).

Answer:

The slope \(m\) of a line is given by the formula \(m = \frac{\text{rise}}{\text{run}}\), where the "rise" is the vertical change and the "run" is the horizontal change between two points on the line. This formula is derived from the geometric relationship in the rate triangle (a right - triangle formed between two points on the line), with the vertical side of the triangle corresponding to the "rise" and the horizontal side corresponding to the "run".