Find the slope of the line satisfying the given conditions. See Example 5. through (-3, 4) and (2, -8)

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 \((-3, 4)\) to \((x_1, y_1)\) and the coordinates of the second point \((2, -8)\) to \((x_2, y_2)\).
3. Substitute the values into the slope formula: \( m = \frac{-8 - 4}{2 - (-3)} \).
4. Simplify the numerator: \(-8 - 4\).
5. Simplify the denominator: \(2 - (-3)\).

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 found 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 analyzing lines and their slopes.

Linear Equation

A linear equation represents a straight line in a coordinate plane and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept. The equation describes the relationship between the x and y coordinates of points on the line. Recognizing the form of a linear equation helps in understanding how to derive the slope from given points.