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 42
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
Observe the graph and identify the points where the line intersects the x-axis and y-axis. These are the x-intercept and y-intercept, respectively.
To determine the x-intercept, locate the point where the line crosses the x-axis. On the x-axis, the y-coordinate is always 0. From the graph, the line intersects the x-axis at x = 3.
To determine the y-intercept, locate the point where the line crosses the y-axis. On the y-axis, the x-coordinate is always 0. From the graph, the line intersects the y-axis at y = 7.
Summarize the intercepts: The x-intercept is the point (3, 0), and the y-intercept is the point (0, 7).
Verify the intercepts by checking the graph again to ensure the points align with the tick marks and the line's trajectory.
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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 intersects the x-axis. At this point, the value of y is zero. To find the x-intercept, you can set the equation of the graph to zero and solve for x. In the provided graph, the x-intercept is at (3, 0).
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Graphing Intercepts
Y-Intercept
The y-intercept of a graph is the point where the graph intersects the y-axis. At this point, the value of x is zero. To determine the y-intercept, set the equation of the graph to zero and solve for y. In the given graph, the y-intercept is at (0, 7).
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04:08Graphing Intercepts
Graph Interpretation
Interpreting a graph involves understanding the relationship between the variables represented on the axes. The x-axis typically represents the independent variable, while the y-axis represents the dependent variable. Analyzing the graph allows you to identify key features such as intercepts, slopes, and overall trends, which are essential for solving related algebraic problems.
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02:16Graphs and Coordinates - Example
Related Practice
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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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In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 3 - √-7)2
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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
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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