Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
2. Graphs of Equations
Two-Variable Equations
0:54 minutes
Problem 42
Textbook Question
Textbook QuestionIn Exercises 41–46, 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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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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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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Graph Interpretation
Interpreting a graph involves understanding the relationship between the variables represented on the axes. In this case, the graph represents a linear equation, and analyzing its intercepts helps in understanding the behavior of the equation. The slope and intercepts provide insights into the function's characteristics, such as its direction and steepness.
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