Linear Equation: Find Line Through Point (2,2) at 180 Degrees

To solve this problem, we'll find the equation of a line passing through $(2,2)$ that makes an angle of $180^\circ$ with the positive x-axis.

• Step 1: Calculate the Slope.
  The slope $m$ of the line can be found using the tangent of the angle. The angle given is $180^\circ$.
  Therefore, $m = \tan(180^\circ) = 0$.
  This tells us that the line is horizontal.
• Step 2: Apply the Point-Slope Form.
  Since the line is horizontal (slope = 0), it has a constant $y$-value.
  The point given is $(2, 2)$, meaning the line's equation is $y = 2$.

Thus, the equation of the line is $y = 2$. This corresponds to choice $4$ in the given options, confirming that it meets all criteria of the problem.

Therefore, the solution to the problem is $y = 2$.