Math Problem Statement

Find the x- and y-intercepts of the given graph.

Solution

In the graph shown in the images, you are asked to find the x-intercept and y-intercept of the given graph. Here's how to analyze it:

Step-by-Step Analysis:

  1. Y-Intercept: The point where the graph crosses the y-axis. From the image, the graph crosses the y-axis at y=2y = 2. Hence, the y-intercept is (0,2)(0, 2).

  2. X-Intercept: The point where the graph crosses the x-axis. Based on the graph, the line does not cross the x-axis at any point. Therefore, there is no x-intercept.

Conclusion:

  • The correct choice from the options would be:
    • No x-intercept
    • yy-intercept: (0,2)(0, 2)

Let me know if you need more details or clarifications! Here are 5 related questions that could expand your understanding:

  1. How would you calculate the x- and y-intercepts if the equation of the line were given?
  2. What happens to the intercepts if the line passes through the origin?
  3. Can a line have more than one x- or y-intercept? Why or why not?
  4. How are intercepts related to the slope of a line?
  5. How would you find the intercepts of a quadratic function?

Tip: When looking for intercepts, remember that the x-intercept occurs when y=0y = 0 and the y-intercept occurs when x=0x = 0.

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Math Problem Analysis

Mathematical Concepts

Algebra
Graphing
Coordinate Geometry

Formulas

x-intercept: set y = 0, y-intercept: set x = 0

Theorems

Intercept Theorem
Basic Linear Graphing

Suitable Grade Level

Grade 8-10