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The problem you're working on asks for the graph of the equation \(7x - 4y = 0\), with the condition that \(x \geq 0\), and requires identifying the graph with the least positive angle \( \theta \) in standard position.

Let's break it down:

1. **Rearranging the equation**: Solve for \(y\):
   \[
   7x - 4y = 0 \quad \Rightarrow \quad y = \frac{7}{4}x
   \]
   This is a linear equation with slope \( \frac{7}{4} \). The line passes through the origin and has a positive slope, indicating that the angle \( \theta \) will be in the first quadrant.

2. **Identifying the least positive angle**: 
   - The angle \( \theta \) formed by the line with the positive x-axis corresponds to the slope of the line.
   - The least positive angle \( \theta \) occurs when the line is closest to the positive x-axis, which means the angle will be small but positive.
   - In standard position, the terminal side of the angle should lie in the first quadrant, as \(x \geq 0\).

3. **Evaluating the graphs**:
   - **Option A** shows a line with a positive slope, which is in the first quadrant and close to the x-axis. This matches the equation's characteristics.
   - **Option B** shows a line in the second quadrant, where the angle would be obtuse (greater than 90°).
   - **Option C** shows a line in the fourth quadrant, but the problem asks for the least *positive* angle, so this would not be correct.

Thus, the correct choice for the graph representing the least positive angle \( \theta \) is **Option A**.

Do you have any questions or want further details on the explanation?

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Here are 5 related questions for further exploration:
1. How do you find the slope of a line given its equation in standard form?
2. What is the significance of the sign of the slope in determining the quadrant of the angle?
3. How can we use trigonometric functions to find the angle from the slope?
4. What happens to the graph if the slope was negative instead?
5. How would you graph this equation if there were no restrictions on \(x\)?

**Tip:** When identifying angles in standard position, always check which quadrant the terminal side of the angle lies in based on the sign of the slope or the direction of the line.

An equation shown below for the terminal side of an angle θ in standard position is given with a restriction on x. Sketch the least positive such angle θ, and find the values of the six trigonometric functions of θ. 7x - 4y = 0, x ≥ 0.

Solve the equation 7x - 4y = 0 and sketch the graph to find the least positive angle θ in standard position. Learn how to determine the values of the six trigonometric functions based on the slope and angle. Suitable for students in Grades 9-11.

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