Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 42

Chapter 3, Problem 42

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

Verified step by step guidance

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: First point: $(-3, 4)$ so $x_1 = -3$ and $y_1 = 4$ Second point: $(2, -8)$ so $x_2 = 2$ and $y_2 = -8$

Substitute the values into the slope formula: \[m = \frac{-8 - 4}{2 - (-3)}\]

Simplify the numerator and denominator separately: Numerator: $-8 - 4 = -12$ Denominator: $2 - (-3) = 2 + 3 = 5$

Write the simplified slope expression: \[m = \frac{-12}{5}\] This fraction represents the slope of the line passing 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 using ordered pairs (x, y). Understanding how to identify and use these points is essential for calculating slope, as the differences in their x and y values determine the line's steepness.

Slope Interpretation

Interpreting the slope helps understand the line's behavior: a positive slope rises from left to right, a negative slope falls, zero slope is horizontal, and undefined slope is vertical. This interpretation aids in visualizing and verifying the result.

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