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

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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: Point 1: \((2, -2)\) so \(x_1 = 2\) and \(y_1 = -2\) Point 2: \((3, -4)\) so \(x_2 = 3\) and \(y_2 = -4\)

Substitute the values into the slope formula: \[m = \frac{-4 - (-2)}{3 - 2}\]

Simplify the numerator and denominator separately: Numerator: \(-4 - (-2) = -4 + 2\) Denominator: \(3 - 2 = 1\)

Write the simplified fraction for the slope: \[m = \frac{-4 + 2}{1}\] This fraction represents the slope of the line through the two points.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are coordinates of the points.

Coordinate Points

Coordinate points represent specific locations on the Cartesian plane, expressed as (x, y). 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.

Undefined Slope

A line has an undefined slope when the change in x (run) is zero, meaning the line is vertical. In such cases, the slope formula results in division by zero, indicating no defined slope exists for vertical lines.

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