Find the Equation: Line Parallel to y=4 Passing Through (1,2)

To solve this problem, we'll follow these steps:

• Step 1: Identify the key characteristics of the line parallel to $y = 4$.
• Step 2: Use the point $(1,2)$ to determine the new horizontal line equation.
• Step 3: Write the equation based on the consistent y-value of the line.

Now, let's work through each step:

Step 1: The given line $y = 4$ is a horizontal line. All horizontal lines have equations in the form $y = c$, where $c$ is a constant value describing the uniform y-position of the line.

Step 2: A line parallel to $y = 4$ that also passes through the point $(1,2)$ would maintain a constant y-value. Since it must pass through $(1,2)$, its y-intercept is $y = 2$.

Step 3: Therefore, the equation of the line parallel to $y = 4$ through $(1,2)$ is simply $y = 2$. This ensures it parallels the horizontal direction.

Thus, the algebraic representation of the line parallel to $y=4$ and passing through the point $(1,2)$ is $y = 2$.