https://file.aiquickdraw.com/mathbot/file/1726755000876ukzw5yqz.jpg

Let's analyze the graph and the problem.

### A. Approximate Coordinates of Intersection:
By looking at the point where the two lines cross on the graph, we can estimate the intersection point. The orange line starts from below the origin (negative slope), and the blue line has a positive slope.

From the visual estimation of the graph, it seems that the intersection occurs around **(4, 5)**.

### B. Verifying the Coordinates:
To verify if the estimated point (4, 5) is the solution to both lines, we would need the equations of the lines. By plugging the point (4, 5) into the equations of both lines, we can check if it satisfies them. If the point satisfies both equations, it is the correct solution.

Without exact line equations, a general verification could be made through the graph's context.

### C. Refining the Approximation:
You can refine the estimate by taking a closer look at the graph and zooming in on the lines to find a more accurate intersection point. One efficient way to find the intersection would be to use the algebraic method of solving the system of linear equations (if the equations are known) to get the exact solution instead of relying on graphical approximation.

Do you want further details on verifying the solution or refining the approximation? 

Here are some related questions for practice:
1. How can you write the equation of a line using its slope and y-intercept?
2. How would you solve two linear equations algebraically to find the intersection point?
3. What is the difference between solving equations graphically and algebraically?
4. How does changing the slope of a line affect its intersection point with another line?
5. Can lines with the same slope intersect? Why or why not?

**Tip**: When solving graphically, always double-check the accuracy of your estimated points by algebraic methods, especially for real-world applications.

The graph shows two lines that intersect at one point. A. What are the approximate coordinates of the point of intersection? B. How could you verify whether the coordinates you estimated are, in fact, the solution? Is the point the solution to the equations of both lines? C. Analyze and Persevere. Use your result to refine your approximation, and try again. Can you find the point of intersection this way? Is there a more efficient way?

Learn how to estimate the point of intersection of two lines by graphing and verifying your solution. This problem explores linear equations, graphing, and solving systems of equations, suitable for students in Grades 8-10.

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