1. We are asked to find the equation of the tangent line $t$ to the graph of the function $f(x) = x^2$ at the point $P(-3, 9)$. 2. The formula for the tangent line to a function $f(x)$ at a point $x=a$ is: $$y = f'(a)(x - a) + f(a)$$ where $f'(a)$ is the derivative of $f(x)$ evaluated at $x=a$. 3. First, find the derivative of $f(x) = x^2$: $$f'(x) = 2x$$ 4. Evaluate the derivative at $x = -3$: $$f'(-3) = 2 \times (-3) = -6$$ 5. The slope of the tangent line at $P(-3, 9)$ is $-6$. 6. Using the point-slope form of the line: $$y = -6(x - (-3)) + 9 = -6(x + 3) + 9$$ 7. Simplify the equation: $$y = -6x - 18 + 9 = -6x - 9$$ 8. The equation of the tangent line $t$ is: $$y = -6x - 9$$