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

Verified step by step guidance

1. Identify the formula for the slope of a line given two points: \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
2. Assign the coordinates of the first point \((x_1, y_1) = (2, -2)\) and the second point \((x_2, y_2) = (3, -4)\).
3. Substitute the values into the slope formula: \( m = \frac{-4 - (-2)}{3 - 2} \).
4. Simplify the numerator: \(-4 - (-2)\) becomes \(-4 + 2\).
5. Simplify the expression to find the slope \( m \).

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.