Find the slope of the line satisfying the given conditions. through (2, -1) and (-3, -3)

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Recall that the slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula: \[m = \frac{y_2 - y_1}{x_2 - x_1}\]

Identify the coordinates of the two points given: \((2, -1)\) and \((-3, -3)\). Here, let \((x_1, y_1) = (2, -1)\) and \((x_2, y_2) = (-3, -3)\).

Substitute the coordinates into the slope formula: \[m = \frac{-3 - (-1)}{-3 - 2}\]

Simplify the numerator and denominator separately: Numerator: \(-3 - (-1) = -3 + 1\) Denominator: \(-3 - 2\)

Write the simplified fraction for the slope: \[m = \frac{-3 + 1}{-3 - 2}\] This fraction represents the slope of the line passing through the two points.

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주요 개념

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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. It is often represented by 'm' and found using the formula m = (y2 - y1) / (x2 - x1).

Coordinate Points

Coordinate points are pairs of numbers (x, y) that represent positions on the Cartesian plane. Understanding how to use these points is essential for calculating slope, as the differences in their x and y values determine the line's steepness.

Slope Formula Application

Applying the slope formula involves substituting the coordinates of two given points into m = (y2 - y1) / (x2 - x1). Careful substitution and simplification yield the slope, which describes the line passing through those points.