Find the slope of each line, provided that it has a slope. through (8, 7) and (1/2, -2)

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 determined using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two 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 Equations

Linear equations represent relationships between variables that graph as straight lines on a coordinate plane. The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Recognizing that the slope is a constant value in linear equations helps in understanding how changes in x affect y, which is crucial for solving problems involving slope.