1. **State the problem:** Find the equation of the line passing through the points $(1,5)$ and $(3,-7)$ in slope-intercept form $y=mx+b$. 2. **Formula for slope:** The slope $m$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1,y_1)=(1,5)$ and $(x_2,y_2)=(3,-7)$. 3. **Calculate the slope:** $$m=\frac{-7 - 5}{3 - 1}=\frac{-12}{2}=-6$$ 4. **Use point-slope form:** $$y - y_1 = m(x - x_1)$$ Substitute $m=-6$ and point $(1,5)$: $$y - 5 = -6(x - 1)$$ 5. **Simplify to slope-intercept form:** $$y - 5 = -6x + 6$$ Add 5 to both sides: $$y = -6x + 6 + 5$$ $$y = -6x + 11$$ 6. **Final answer:** The equation of the line in slope-intercept form is $$y = -6x + 11$$.