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

Two-Variable Equations

College Algebra

2. Graphs of Equations

Two-Variable Equations

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1:48 minutes

Problem 15

Textbook Question

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

Verified step by step guidance

Start by understanding the equation y = x - 2. This is a linear equation, meaning its graph will be a straight line. The slope of the line is 1 (the coefficient of x), and the y-intercept is -2 (the constant term).

Create a table of values for x and y. Use the given x-values: -3, -2, -1, 0, 1, 2, 3. For each x-value, substitute it into the equation y = x - 2 to calculate the corresponding y-value.

For example, when x = -3, substitute into the equation: y = -3 - 2. Similarly, calculate y for all other x-values (-2, -1, 0, 1, 2, 3). Record these (x, y) pairs in the table.

Plot the points from the table on a coordinate plane. Each (x, y) pair represents a point on the graph. For example, if one pair is (-3, -5), plot the point at x = -3 and y = -5.

Draw a straight line through all the plotted points. Since this is a linear equation, the points should align perfectly in a straight line. Label the graph with the equation 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 and the y-intercept is -2, indicating that the line rises one unit for every unit it moves to the right.

Graphing Points

Graphing points involves plotting specific coordinates on a Cartesian plane, where each point is defined by an x-value and a corresponding y-value. For the equation y = x - 2, you can calculate y for each given x value (-3, -2, -1, 0, 1, 2, 3) to find the points to plot. For example, when x = 0, y = -2, resulting in the point (0, -2).

Slope-Intercept Form

The slope-intercept form of a linear equation is a way to express the relationship between x and y, highlighting the slope and y-intercept. This form is useful for quickly identifying how steep the line is and where it crosses the y-axis. In y = x - 2, the slope of 1 indicates a 45-degree angle, while the y-intercept of -2 shows where the line intersects the y-axis.