1. **State the problem:** Find the x-intercept and y-intercept of the function $$y=\frac{5x}{x-1}$$. 2. **Recall definitions:** - The x-intercept occurs where $$y=0$$. - The y-intercept occurs where $$x=0$$. 3. **Find the x-intercept:** Set $$y=0$$: $$0=\frac{5x}{x-1}$$ For a fraction to be zero, the numerator must be zero (and denominator not zero): $$5x=0 \implies x=0$$ Check denominator at $$x=0$$: $$0-1=-1 \neq 0$$, so valid. 4. **Find the y-intercept:** Set $$x=0$$: $$y=\frac{5\cdot 0}{0-1}=\frac{0}{-1}=0$$ 5. **Summary:** - x-intercept: $$(0,0)$$ - y-intercept: $$(0,0)$$ Both intercepts are at the origin.