1. **State the problem:** We need to find the equation of the tangent line to the curve given by $$f(x) = x^2 - 4$$ at the point where $$x = 1$$. 2. **Recall the formula for the tangent line:** The equation of the tangent line to a function $$f(x)$$ at $$x = a$$ is given by: $$ y = f(a) + f'(a)(x - a) $$ where $$f'(a)$$ is the derivative of $$f(x)$$ evaluated at $$x = a$$. 3. **Find the derivative of $$f(x)$$:** $$ f'(x) = \frac{d}{dx}(x^2 - 4) = 2x $$ 4. **Evaluate $$f(1)$$ and $$f'(1)$$:** $$ f(1) = 1^2 - 4 = 1 - 4 = -3 $$ $$ f'(1) = 2 \times 1 = 2 $$ 5. **Write the equation of the tangent line:** $$ y = f(1) + f'(1)(x - 1) = -3 + 2(x - 1) $$ 6. **Simplify the equation:** $$ y = -3 + 2x - 2 = 2x - 5 $$ **Final answer:** The equation of the tangent line at $$x = 1$$ is $$y = 2x - 5$$.