Find the slope of each line, provided that it has a slope. through (0, -7) and (3, -7)

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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: \((0, -7)\) and \((3, -7)\). Here, \(x_1 = 0\), \(y_1 = -7\), \(x_2 = 3\), and \(y_2 = -7\).

Substitute the values into the slope formula: \[m = \frac{-7 - (-7)}{3 - 0}\]

Simplify the numerator and denominator separately: Numerator: \(-7 - (-7) = -7 + 7 = 0\) Denominator: \(3 - 0 = 3\)

Calculate the slope by dividing the simplified numerator by the denominator: \[m = \frac{0}{3}\] This will give you the slope of the line.

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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 change in y-values to the change in x-values between two points. It is given by the formula m = (y2 - y1) / (x2 - x1). A positive slope indicates an upward trend, while a negative slope indicates a downward trend.

Coordinates of Points

Points on the Cartesian plane are represented as ordered pairs (x, y). Understanding how to use these coordinates is essential for calculating slope, as you need the x and y values of two points to find the change in vertical and horizontal distances.

Horizontal Lines and Zero Slope

A horizontal line has the same y-value for all points, meaning there is no vertical change between points. Therefore, its slope is zero because the numerator in the slope formula (change in y) is zero, indicating a flat line.