Table of contents

0. Review of Algebra4h 18m
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 22m
10. Combinatorics & Probability1h 45m

2. Graphs of Equations

Two-Variable Equations

College Algebra

2. Graphs of Equations

Two-Variable Equations

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0:54 minutes

Problem 42

Textbook Question

In 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.

Verified step by step guidance

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).

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).

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.