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### Problem Breakdown:
1. **Equation**: \(-6x - 2y = 0\), with the restriction \(x \leq 0\).
2. The goal is to:
   - Find the least positive angle \(\theta\) for which this equation represents the terminal side of the angle in standard position.
   - Determine the values of the six trigonometric functions for \(\theta\).
   - Choose the graph corresponding to this equation with the least positive angle \(\theta\).

### Solving for the Equation and the Angle:
1. **Rewriting the equation**: \(-6x - 2y = 0\) can be rewritten as:
   \[
   2y = -6x
   \]
   \[
   y = -3x
   \]
   This is a straight line with a slope of \(-3\), passing through the origin (since there's no constant term).

2. **Identifying the angle**:
   - The slope of the line is \(-3\), so the terminal side of the angle lies in Quadrant II because the restriction is \(x \leq 0\) (i.e., we are looking for a graph that covers negative \(x\)).
   - The angle \(\theta\) can be found using the inverse tangent function. The slope \(-3\) corresponds to:
     \[
     \theta = \tan^{-1}(-3)
     \]
     which will give an angle in Quadrant II.

### Identifying the Graph:
- **Quadrant II** behavior means we expect the line to rise as it moves to the left along the \(x\)-axis (i.e., \(x \leq 0\)).
- Let's match the graphs with this understanding:
  - **Option A**: Shows a line in Quadrant IV, which does not match our expectations.
  - **Option B**: Shows a line in Quadrant II, which fits our equation's behavior.
  - **Option C**: Shows a parabola, which does not match our equation (since it's linear).

Thus, **Option B** is the correct graph for the given equation.

Would you like further details on how to calculate the six trigonometric functions or any additional clarifications? 

### Related Questions:
1. How do you calculate the six trigonometric functions given an angle?
2. What is the process for finding the angle using the inverse tangent?
3. How does the slope of a line relate to its angle in standard position?
4. What are the typical signs of trigonometric functions in different quadrants?
5. How would the graph change if the restriction on \(x\) were different?

### Tip:
When finding the angle for a line, always check its slope and consider which quadrant the line passes through based on restrictions like \(x \leq 0\) or \(x \geq 0\).

An equation for the terminal side of an angle θ in standard position is given as -6x - 2y = 0 with a restriction x ≤ 0. Sketch the least positive angle θ, and find the values of the six trigonometric functions of θ. Choose the graph with the least positive angle θ.

Solve for the least positive angle θ using the equation -6x - 2y = 0 with a restriction x ≤ 0. Understand how to compute trigonometric functions based on the slope of the line and choose the correct graph corresponding to the equation. Suitable for high school students in Grades 9-12.

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