Textbook Question
In Exercises 1–26, solve and check each linear equation. 3(x - 8) = x
2
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 2, Problem 15a
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = x - 2
Verified step by step guidance1
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.
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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).
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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.
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Related Practice
Textbook Question
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(6x + 1) = x - 1
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In Exercises 1–26, solve and check each linear equation. 4(x + 9) = x
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In Exercises 15–26, use graphs to find each set. (- 3, 0) ∩ [- 1, 2]
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Solve each equation in Exercises 15–34 by the square root property.
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After a 20% reduction, you purchase a television for \$336. What was the television's price before the reduction?