Textbook Question
In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 1 - x/2 > 4
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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 41a
Use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.
Verified step by step guidance1
Step 1: Observe the graph and identify the x-intercept. The x-intercept is the point where the graph crosses the x-axis. From the graph, the orange line crosses the x-axis at x = -5. This means the x-intercept is (-5, 0).
Step 2: Observe the graph and identify the y-intercept. The y-intercept is the point where the graph crosses the y-axis. From the graph, the orange line crosses the y-axis at y = 5. This means the y-intercept is (0, 5).
Step 3: Understand the significance of intercepts. The x-intercept represents the value of x when y = 0, and the y-intercept represents the value of y when x = 0. These points are useful for understanding the behavior of the graph.
Step 4: Verify the intercepts by checking the tick marks along the axes. Each tick mark represents one unit, so the x-intercept at (-5, 0) and the y-intercept at (0, 5) are consistent with the graph.
Step 5: Use the intercepts to write the equation of the line if needed. The slope can be calculated using the formula m = (change in y) / (change in x). From the graph, the slope is m = (5 - 0) / (0 - (-5)) = 5/5 = 1. The equation of the line can be written as y = mx + b, where m is the slope and b is the y-intercept.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
X-Intercept
The x-intercept of a graph is the point where the graph crosses the x-axis. At this point, the value of y is zero. To find the x-intercept, you can set the equation of the line to zero and solve for x. In the provided graph, the x-intercept is located at (-5, 0).
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Graphing Intercepts
Y-Intercept
The y-intercept of a graph is the point where the graph crosses the y-axis. At this point, the value of x is zero. To determine the y-intercept, you set the equation of the line to zero and solve for y. In the given graph, the y-intercept is at (0, 5).
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Graph Interpretation
Interpreting a graph involves understanding the relationship between the x and y coordinates represented visually. This includes identifying key features such as intercepts, slopes, and the overall shape of the graph. In this case, recognizing the intercepts helps in analyzing the behavior of the linear function depicted in the graph.
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Related Practice
Textbook Question
In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.
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Textbook Question
Use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.
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Textbook Question
Solve each equation in Exercises 41–60 by making an appropriate substitution.
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Textbook Question
In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. x/4 - 3/2 ≤ x/2 + 1
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Textbook Question
In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? E = mc2 for m
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