1. **State the problem:** Find the intercepts of the line given by the equation $$y = 5x - 13$$. 2. **Recall the intercept definitions:** - The **y-intercept** is the point where the line crosses the y-axis, so $x=0$. - The **x-intercept** is the point where the line crosses the x-axis, so $y=0$. 3. **Find the y-intercept:** Substitute $x=0$ into the equation: $$y = 5(0) - 13 = 0 - 13 = -13$$ So the y-intercept is at the point $\boxed{(0, -13)}$. 4. **Find the x-intercept:** Substitute $y=0$ into the equation: $$0 = 5x - 13$$ Add 13 to both sides: $$13 = 5x$$ Divide both sides by 5: $$x = \frac{13}{5}$$ Show cancellation: $$x = \cancel{\frac{13}{\cancel{5}}}$$ So the x-intercept is at the point $\boxed{\left(\frac{13}{5}, 0\right)}$. **Final answers:** - y-intercept: $(0, -13)$ - x-intercept: $\left(\frac{13}{5}, 0\right)$