Table of contents

0. Review of Algebra4h 16m
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 19m
10. Combinatorics & Probability1h 45m

2. Graphs of Equations

Graphs and Coordinates

College Algebra

2. Graphs of Equations

Graphs and Coordinates

1:48 minutes

Problem 16

Textbook Question

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3 y = x + 2

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Linear Equations

A linear equation is an algebraic expression that represents a straight line when graphed on a coordinate plane. It typically takes the form y = mx + b, where m is the slope and b is the y-intercept. In the given equation y = x + 2, the slope is 1, indicating that for every unit increase in x, y increases by the same amount.

Graphing Points

Graphing points involves plotting specific coordinates on a Cartesian plane, where the x-coordinate represents the horizontal position and the y-coordinate represents the vertical position. For the equation y = x + 2, you can calculate y for each given x value (-3, -2, -1, 0, 1, 2, 3) to find corresponding points, which can then be plotted to visualize the linear relationship.

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m is the slope and b is the y-intercept. This form is particularly useful for quickly identifying the slope and y-intercept of a line, allowing for easy graphing. In the equation y = x + 2, the slope is 1 and the y-intercept is 2, indicating that the line crosses the y-axis at (0, 2).