1. **Stating the problem:** We need to find the equation of a line first using the point-slope form and then convert it to slope-intercept form. 2. **Point-slope form formula:** The point-slope form of a line is given by: $$y - y_1 = m(x - x_1)$$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line. 3. **Slope-intercept form formula:** The slope-intercept form is: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 4. **Example:** Suppose we have a point $(2, 3)$ and slope $m = 4$. 5. **Apply point-slope form:** $$y - 3 = 4(x - 2)$$ 6. **Simplify:** $$y - 3 = 4x - 8$$ 7. **Solve for $y$ to get slope-intercept form:** $$y = 4x - 8 + 3$$ $$y = 4x - 5$$ 8. **Explanation:** We started with the point-slope form using the given point and slope, then simplified and rearranged to get the slope-intercept form, which is easier to graph and interpret. **Final answer:** The equation of the line in slope-intercept form is: $$y = 4x - 5$$