Textbook Question
In Exercises 9–20, find each product and write the result in standard form. (5 - 2i)2
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 19a
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = -(1/2)x
Verified step by step guidance1
Start by understanding the equation y = -(1/2)x. This is a linear equation where the slope is -1/2 and the y-intercept is 0. The slope indicates that for every 1 unit increase in x, y decreases by 1/2.
Create a table of values for the given x-values: x = -3, -2, -1, 0, 1, 2, 3. For each x-value, substitute it into the equation y = -(1/2)x to calculate the corresponding y-value.
For example, when x = -3, substitute into the equation: y = -(1/2)(-3). Simplify to find the y-value. Repeat this process for all other x-values.
Once you have the table of x and y values, plot these points on a coordinate plane. Each point will have coordinates (x, y) based on your calculations.
After plotting all the points, draw a straight line through them. This line represents the graph of the equation y = -(1/2)x. Ensure the line extends in both directions and label the axes 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 the relationship between the variables and predict the behavior of the line.
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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 = -(1/2)x, the slope is -1/2, indicating a downward slope, and the y-intercept is 0, meaning the line passes through the origin.
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Graphing Points
Graphing points involves plotting specific coordinates (x, y) on a Cartesian plane to visualize the relationship defined by an equation. For the equation y = -(1/2)x, substituting values for x (like -3, -2, -1, 0, 1, 2, 3) allows us to calculate corresponding y values, which can then be plotted to form the line. This process is crucial for understanding how changes in x affect y.
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Related Practice
Textbook Question
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = - (1/2)x + 2
Textbook Question
Solve each radical equation in Exercises 11–30. Check all proposed solutions.
Textbook Question
Find each product and write the result in standard form. (2 + 3i)2
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Textbook Question
Solve and check each linear equation. 2(x - 1) + 3 = x - 3(x + 1)
Textbook Question
In Exercises 15–26, use graphs to find each set. (- ∞, 5) ∩ [1, 8)