Ch. 2 - Graphs and Functions

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

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 41

Chapter 3, Problem 41

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

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: $(2, -1)$ 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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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 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.

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