https://file.aiquickdraw.com/mathbot/file/17265354862901zxxpb2h.jpg

In the image, the task asks you to solve the equation \(\sqrt{3x} = 3.1\) by graphing. The equation is written in the form \( f(x) = \sqrt{ax} \) and \( g(x) = k \), where \(a = 3\) and \(k = 3.1\).

### To solve this by graphing:

1. **Graph the function** \( f(x) = \sqrt{3x} \).
   - This graph is a square root function starting at \( x = 0 \).
   
2. **Graph the line** \( g(x) = 3.1 \), which is a horizontal line at \(y = 3.1\).

3. **Find the intersection point** of the graph of \( f(x) \) and the line \( g(x) = 3.1 \).
   - According to the image, the intersection happens at approximately \( x = 3.33 \).
   
Thus, the solution to \(\sqrt{3x} = 3.1\) is approximately:
\[
x \approx 3.33
\]

Would you like more details on graphing techniques or further explanations on how to calculate the intersection algebraically?

### Follow-up Questions:
1. How do you graph square root functions like \( f(x) = \sqrt{3x} \)?
2. What are the steps to find intersections between curves and lines?
3. How can you solve \( \sqrt{3x} = 3.1 \) algebraically?
4. What tools can you use to graph functions accurately?
5. Why do square root functions have limited domains?

### Tip:
For square root functions, remember that the function is only defined for non-negative values of \(x\), so your graph will only start from \(x = 0\).

Solve the following equation by graphing. Round your answer to 2 decimal places: sqrt(2x - 2) = 3

Learn how to solve square root equations like sqrt(2x - 2) = 3 by graphing. This lesson covers graphing techniques for square root functions and finding intersections with horizontal lines. Suitable for high school students in Grades 9-12.

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