1. **State the problem:** Find the intersection point of the two lines given by the equations $y=3$ and $y=\frac{1}{4}x + 5$. 2. **Use the formula:** At the intersection, the $y$ values of both lines are equal. So, set the equations equal: $$3 = \frac{1}{4}x + 5$$ 3. **Solve for $x$:** $$3 = \frac{1}{4}x + 5$$ Subtract 5 from both sides: $$3 - 5 = \frac{1}{4}x + 5 - 5$$ $$-2 = \frac{1}{4}x$$ Multiply both sides by 4 to isolate $x$: $$4 \times (-2) = 4 \times \frac{1}{4}x$$ $$-8 = \cancel{4} \times \frac{1}{\cancel{4}} x$$ $$-8 = x$$ 4. **Find $y$ coordinate:** Substitute $x = -8$ into either equation. Using $y=3$ (already given), so $y=3$. 5. **Check the solution:** Substitute $x=-8$ into $y=\frac{1}{4}x + 5$: $$y = \frac{1}{4}(-8) + 5 = -2 + 5 = 3$$ Matches the other line's $y$ value, so the intersection point is correct. **Final answer:** The lines intersect at the point $$(-8, 3)$$.