what is the equation of the line that is parallel to the given line and passes through the point (-4,-6)?\no…

Answer:

C. $y = -6$

Explanation:

Step1: Find the equation of the given line.

The given line passes through points $(-8, 4)$ and $(8, 4)$. Since the y-coordinates are the same, the line is horizontal. The equation is $y = 4$.

Step2: Determine the slope of the required line.

Parallel lines have the same slope. The slope of the horizontal line $y = 4$ is $m = 0$. Therefore, the required line must also have a slope of $0$.

Step3: Identify the form of the required line's equation.

A line with a slope of $0$ is a horizontal line. Its equation is of the form $y = k$, where $k$ is a constant.

Step4: Use the given point to find the constant $k$.

The required line passes through the point $(-4, -6)$. For a horizontal line $y = k$, all points on the line must have the y-coordinate $k$. Thus, $k = -6$.

Step5: Write the equation of the required line.

Substituting $k = -6$ into the form $y = k$, the equation of the required line is $y = -6$.