Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

2. Graphs of Equations

Lines

College Algebra

2. Graphs of Equations

Lines

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1:18 minutes

Problem 143

Textbook Question

Exercises 143–145 will help you prepare for the material covered in the next section. If (x1,y1) = (-3, 1) and (x2, y2) = (−2, 4), find (y2-y1)/(x2-x1)

Verified step by step guidance

Identify the given points: \((x_1, y_1) = (-3, 1)\) and \((x_2, y_2) = (-2, 4)\).

Recall the formula for the slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\): \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Substitute the given values into the formula: \(m = \frac{4 - 1}{-2 - (-3)}\).

Simplify the numerator: \(4 - 1\).

Simplify the denominator: \(-2 - (-3)\).

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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 change in the y-coordinates divided by the change in the x-coordinates between two points. It is represented by the formula m = (y2 - y1) / (x2 - x1). A positive slope indicates the line rises from left to right, while a negative slope indicates it falls.

Coordinate System

A coordinate system is a two-dimensional plane defined by an x-axis (horizontal) and a y-axis (vertical). Each point on this plane is represented by an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position. Understanding how to plot points and interpret their coordinates is essential for analyzing relationships between variables.

Ordered Pairs

Ordered pairs are pairs of numbers used to represent points in a coordinate system, typically written as (x, y). The first number corresponds to the x-coordinate, and the second number corresponds to the y-coordinate. In the context of the question, the points (-3, 1) and (-2, 4) are used to calculate the slope, illustrating how changes in x relate to changes in y.