1. **State the problem:** Find the equation of the line that passes through the points $(0,-5)$ and $(4,3)$. 2. **Formula used:** The slope $m$ of a line passing through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$m=\frac{y_2-y_1}{x_2-x_1}$$ 3. **Calculate the slope:** $$m=\frac{3-(-5)}{4-0}=\frac{3+5}{4}=\frac{8}{4}$$ 4. **Simplify the slope:** $$m=\frac{\cancel{8}}{\cancel{4}}=2$$ 5. **Use point-slope form:** The equation of the line is: $$y-y_1=m(x-x_1)$$ Using point $(0,-5)$: $$y-(-5)=2(x-0)$$ 6. **Simplify the equation:** $$y+5=2x$$ $$y=2x-5$$ **Final answer:** The equation of the line passing through $(0,-5)$ and $(4,3)$ is: $$y=2x-5$$