1. **State the problem:** Find the slope of the tangent line and the equation of the tangent line for the function $f(x) = 3x + 4$ at the point $(1,7)$. 2. **Recall the formula for the slope of the tangent line:** The slope of the tangent line to the curve at a point is given by the derivative $f'(x)$ evaluated at that point. 3. **Find the derivative:** Since $f(x) = 3x + 4$, the derivative is $$f'(x) = \frac{d}{dx}(3x + 4) = 3.$$ 4. **Evaluate the slope at $x=1$:** $$f'(1) = 3.$$ So, the slope of the tangent line at $(1,7)$ is 3. 5. **Use the point-slope form of a line:** $$y - y_1 = m(x - x_1),$$ where $m$ is the slope and $(x_1,y_1)$ is the point on the line. 6. **Plug in the values:** $$y - 7 = 3(x - 1).$$ 7. **Simplify the equation:** $$y - 7 = 3x - 3,$$ $$y = 3x + 4.$$ **Final answer:** The slope of the tangent line at $(1,7)$ is 3, and the equation of the tangent line is $y = 3x + 4$.