Step 1 :Given a point (-2,-3) and a line with the equation \(y=-\frac{1}{2} x-1\), we need to find the equation of a line that passes through the given point and is parallel to the given line.
Step 2 :Since parallel lines have the same slope, the slope \(m\) of the line we are looking for is also -1/2.
Step 3 :Substitute the point (-2,-3) into the equation \(y = mx + b\) to solve for \(b\).
Step 4 :Substituting gives us \(-3 = -\frac{1}{2}*(-2) + b\), which simplifies to \(-3 = 1 + b\).
Step 5 :Solving for \(b\) gives us \(b = -4\).
Step 6 :So, the equation of the line is \(y = -\frac{1}{2}x - 4\).
Step 7 :Final Answer: The equation of the line is \(\boxed{y = -\frac{1}{2}x - 4}\).