1. **State the problem:** Find the equation of the tangent line to the function $y = 2x + 5$ at the point $(-1, 3)$. 2. **Recall the formula:** The equation of the tangent line to a function $y = f(x)$ at $x = a$ is given by: $$y = f'(a)(x - a) + f(a)$$ where $f'(a)$ is the derivative of $f(x)$ evaluated at $x = a$. 3. **Find the derivative:** Since $y = 2x + 5$ is a linear function, its derivative is constant: $$f'(x) = 2$$ 4. **Evaluate the derivative at $x = -1$:** $$f'(-1) = 2$$ 5. **Evaluate the function at $x = -1$:** $$f(-1) = 2(-1) + 5 = -2 + 5 = 3$$ 6. **Write the equation of the tangent line:** $$y = 2(x - (-1)) + 3 = 2(x + 1) + 3$$ 7. **Simplify:** $$y = 2x + 2 + 3 = 2x + 5$$ **Final answer:** The equation of the tangent line at $(-1, 3)$ is $$y = 2x + 5$$ This matches the original function, which makes sense because the function is linear and its tangent line at any point is the function itself.