Exercises 143–145 will help you prepare for the material covered in the next section. If (x1,y1) = (-3, 1) and (x2, y2) = (−2, 4), find (y2-y1)/(x2-x1)

Key Concepts

Slope of a Line

The slope of a line measures its steepness and direction, calculated as the change in the y-coordinates divided by the change in the x-coordinates between two points. It is represented by the formula m = (y2 - y1) / (x2 - x1). A positive slope indicates the line rises from left to right, while a negative slope indicates it falls.

Coordinate System

A coordinate system is a two-dimensional plane defined by an x-axis (horizontal) and a y-axis (vertical). Each point on this plane is represented by an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position. Understanding how to plot points and interpret their coordinates is essential for analyzing relationships between variables.

Ordered Pairs

Ordered pairs are pairs of numbers used to represent points in a coordinate system, typically written as (x, y). The first number corresponds to the x-coordinate, and the second number corresponds to the y-coordinate. In the context of the question, the points (-3, 1) and (-2, 4) are used to calculate the slope, illustrating how changes in x relate to changes in y.