Textbook Question
Including a 10.5% hotel tax, your room in San Diego cost \$216.58 per night. Find the nightly cost before the tax was added.
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 16a
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = x + 2
Verified step by step guidance1
Identify the given equation: y = x + 2. This is a linear equation, which means its graph will be a straight line.
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.
Plot the points (x, y) on a coordinate plane. Each pair of x and y values forms a point, such as (-3, -1), (-2, 0), etc.
Draw a straight line through all the plotted points. Since this is a linear equation, the points should align perfectly, forming a straight line.
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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 the relationship between variables and predict values.
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Graphing Points
Graphing points involves plotting specific coordinates on a Cartesian plane, where the x-coordinate indicates the horizontal position and the y-coordinate indicates the vertical position. For the equation y = x + 2, students will calculate y for given x values, such as -3, -2, -1, etc., and plot these points to visualize the linear relationship.
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Slope and Y-Intercept
The slope of a line indicates its steepness and direction, 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, represented by the value of y when x is zero. In the equation y = x + 2, the slope is 1 and the y-intercept is 2, which are crucial for understanding the line's behavior and graphing it accurately.
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Related Practice
Textbook Question
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(6x + 1) = x - 1
Textbook Question
In Exercises 1–26, solve and check each linear equation. 4(x + 9) = x
Textbook Question
Solve each equation in Exercises 15–34 by the square root property.
Textbook Question
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7(x-4) = x + 2
Textbook Question
Find each product and write the result in standard form. (- 5 + i)(- 5 - i)