Textbook Question
In Exercises 9–20, find each product and write the result in standard form. (5 - 2i)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 20a
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = - (1/2)x + 2
Verified step by step guidance1
Step 1: Understand the equation y = -(1/2)x + 2. This is a linear equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Here, the slope m = -(1/2) and the y-intercept b = 2.
Step 2: Create a table of values for x and y. Substitute the given x-values (-3, -2, -1, 0, 1, 2, 3) into the equation y = -(1/2)x + 2 to calculate the corresponding y-values. For example, when x = -3, substitute into the equation to find y.
Step 3: Plot the points (x, y) on a Cartesian coordinate system. Use the x-values and their corresponding y-values from the table to mark the points on the graph.
Step 4: Draw the line through the plotted points. Since this is a linear equation, the points will align in a straight line. Extend the line in both directions, ensuring it passes through all the points.
Step 5: Label the graph. Indicate the slope of the line (-1/2) and the y-intercept (2). Ensure the axes are labeled correctly and the scale is consistent.
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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-Intercept Form
The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope of the line and b represents the y-intercept. The slope indicates the steepness and direction of the line, while the y-intercept is the point where the line crosses the y-axis. This form is particularly useful for quickly identifying key characteristics of the graph.
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Graphing Points
Graphing points involves plotting specific (x, y) coordinates on a Cartesian plane. For the given equation, substituting values of x allows us to calculate corresponding y values, creating a set of points that can be plotted. Understanding how to graph points is crucial for visualizing the relationship between variables in linear equations.
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Related Practice
Textbook Question
In Exercises 15–26, use graphs to find each set. (- ∞, 5) ⋃ [1, 8)
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Textbook Question
In Exercises 21–28, divide and express the result in standard form. 2/(3 - i)
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Textbook Question
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = -(1/2)x
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Textbook Question
Solve and check each linear equation. 2(x - 1) + 3 = x - 3(x + 1)
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Textbook Question
You invested \$20,000 in two accounts paying 1.45% and 1.59% annual interest. If the total interest earned for the year was \$307.50, how much was invested at each rate?
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