Question

determining equations of parallel lines
what is the equation of the line that is parallel to the given line and passes through the given point?
y = -2
x = -2
y = -4
x = -4

Explanation:

Step1: Identify the slope of the given line

The given line is y = 6, which is a horizontal line with slope m = 0.

Step2: Recall the property of parallel lines

Parallel lines have the same slope. So the line parallel to y = 6 also has a slope of 0.

Step3: Use the point - slope form for a horizontal line

The point is (2,-4). For a horizontal line passing through (x₁,y₁)=(2,-4), the equation is of the form y = y₁. So the equation of the line is y=-4.

Answer:

y = - 4