1. **Stating the problem:** We need to sketch the graph of the equation $$2X - y - 3 = 0$$. 2. **Rewrite the equation in slope-intercept form:** Start by isolating $y$: $$2X - y - 3 = 0 \implies -y = -2X + 3 \implies y = 2X - 3$$ 3. **Identify the slope and y-intercept:** The equation is now in the form $y = mX + b$ where: - Slope $m = 2$ - Y-intercept $b = -3$ 4. **Plotting points:** - When $X=0$, $y = 2(0) - 3 = -3$ (point $(0, -3)$) - When $X=1$, $y = 2(1) - 3 = -1$ (point $(1, -1)$) - When $X=2$, $y = 2(2) - 3 = 1$ (point $(2, 1)$) 5. **Draw the line:** Connect these points with a straight line extending in both directions. 6. **Explanation:** The slope $2$ means the line rises 2 units vertically for every 1 unit it moves horizontally to the right. The y-intercept $-3$ means the line crosses the y-axis at $(0, -3)$. **Final answer:** The graph of the equation is the line $$y = 2X - 3$$ with slope 2 and y-intercept -3.