Textbook Question
Solve and check each linear equation. 4x + 9 = 33
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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 1
Graph each equation in Exercises 1–4. Let x= -3, -2. -1, 0, 1, 2 and 3. y = 2x-2
Verified step by step guidance1
Step 1: Understand the equation y = 2x - 2. This is a linear equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Step 2: 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 = 2x - 2 to calculate the corresponding y-value.
Step 3: For example, when x = -3, substitute into the equation: y = 2(-3) - 2. Similarly, calculate y for all other x-values (-2, -1, 0, 1, 2, 3).
Step 4: Once you have the table of x and y values, plot these points on a coordinate plane. Each pair (x, y) represents a point on the graph.
Step 5: Draw a straight line through the plotted points, as the equation represents a linear function. Ensure the line extends in both directions and label the graph appropriately.
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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. Understanding linear equations is essential for graphing, as it allows students to identify how changes in x affect y.
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Slope and Y-Intercept
The slope of a linear equation indicates the steepness and direction of the line, calculated as the change in y over the change in x (rise/run). The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero. In the equation y = 2x - 2, the slope is 2 and the y-intercept is -2, which are crucial for accurately plotting the graph.
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Graphing Points
Graphing points involves plotting specific (x, y) coordinates on a Cartesian plane. For the equation y = 2x - 2, students will substitute the given x-values (-3, -2, -1, 0, 1, 2, 3) to find corresponding y-values. This process helps visualize the relationship between x and y, forming the linear graph of the equation.
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Related Practice
Textbook Question
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle.
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Textbook Question
Solve each equation in Exercises 1 - 14 by factoring.
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Textbook Question
Plot the given point in a rectangular coordinate system. (1, 4)
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Textbook Question
Graph each equation in Exercises 1–4. Let x= -3, -2. -1, 0, 1, 2 and 3. y = x^2-3
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Textbook Question
In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (1, 6]
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