1. **State the problem:** Find the equation of the line passing through the point $(5, 4)$ with slope $2$. 2. **Formula used:** The point-slope form of a line is given by: $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope. 3. **Substitute the given values:** $$y - 4 = 2(x - 5)$$ 4. **Simplify the equation:** $$y - 4 = 2x - 10$$ 5. **Solve for $y$ to get slope-intercept form:** $$y = 2x - 10 + 4$$ $$y = 2x - 6$$ 6. **Final answer:** The equation of the line is: $$y = 2x - 6$$ This means the line has slope $2$ and crosses the y-axis at $-6$.