A line tangent to a circle at a point, is perpendicular to the radius at that point. So
Step 1. Identify the center of the circle.
Step 2. Find the slope (m) (or equation) of the line between the center of the circle and (-3,-1).
Step 3. Solve for the y intercept (b) of the tangent line through the point (-3,-1) by solving the equation below for b, with m equal to the slope above, as the slope of tangent line is the negative reciprocal of that slope. -1 = -(1/m) (-3) + b
Step 4. Equation for the tangent line will be y = -(1/m)x + b
I'll be happy to follow up if you have any problems performing any of these steps. John