Find the slope of each line, provided that it has a slope. through (2, -2) and (3, -4)

Key Concepts

Slope of a Line

The slope of a line measures its steepness and direction, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. It is often represented by the letter 'm' and can be expressed mathematically as m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two distinct points.

Coordinate System

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

Linear Equation

A linear equation represents a straight line in a coordinate system and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept. The equation describes how y changes with respect to x, and knowing the slope allows us to understand the line's behavior and predict values for y given x.