1. **State the problem:** We are given two linear equations: $$y = 2kx + 3$$ and $$3y - 9 = 18x$$ We want to analyze these equations, possibly to find the value of $k$ such that the two lines are equivalent or to find their intersection. 2. **Rewrite the second equation in slope-intercept form:** Start with $$3y - 9 = 18x$$ Add 9 to both sides: $$3y = 18x + 9$$ Divide both sides by 3: $$y = 6x + 3$$ 3. **Compare the two equations:** First equation: $$y = 2kx + 3$$ Second equation: $$y = 6x + 3$$ For the two lines to be the same, their slopes and intercepts must be equal. 4. **Set slopes equal:** $$2k = 6$$ Solve for $k$: $$k = \frac{6}{2} = 3$$ 5. **Conclusion:** The value of $k$ that makes the two lines identical is $k = 3$. **Final answer:** $$k = 3$$