1. **State the problem:** Solve the inequality $$2x - y \geq 1$$ graphically and find at least 6 ordered pairs that satisfy the inequality. 2. **Rewrite the inequality:** To graph the inequality, first express it in terms of $$y$$: $$2x - y \geq 1 \implies -y \geq 1 - 2x \implies y \leq 2x - 1$$ 3. **Graph the boundary line:** The boundary line is given by the equation: $$y = 2x - 1$$ This is a straight line with slope 2 and y-intercept -1. 4. **Plot the boundary line:** - When $$x=0$$, $$y = 2(0) - 1 = -1$$, so point (0, -1). - When $$x=1$$, $$y = 2(1) - 1 = 1$$, so point (1, 1). 5. **Determine the inequality region:** Since the inequality is $$y \leq 2x - 1$$, the solution region is the area **below or on** the line. 6. **Check a test point:** Use point (0,0): $$0 \leq 2(0) - 1 = -1$$ is false, so (0,0) is **not** in the solution region. 7. **Find 6 ordered pairs satisfying $$y \leq 2x - 1$$:** Choose values of $$x$$ and calculate $$y$$ such that $$y \leq 2x - 1$$: - For $$x=0$$, $$y \leq -1$$, e.g., (0, -1), (0, -2) - For $$x=1$$, $$y \leq 1$$, e.g., (1, 1), (1, 0) - For $$x=2$$, $$y \leq 3$$, e.g., (2, 3), (2, 2) **Six ordered pairs:** (0, -1), (0, -2), (1, 1), (1, 0), (2, 3), (2, 2) **Final answer:** The inequality $$2x - y \geq 1$$ is equivalent to $$y \leq 2x - 1$$. The graph is the line $$y = 2x - 1$$ with the solution region below or on this line. Six points satisfying the inequality are (0, -1), (0, -2), (1, 1), (1, 0), (2, 3), and (2, 2).