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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 51
Chapter 3, Problem 51

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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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 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.
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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.
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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.
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