Final answer:
To graph the inequality ½x - 1 ≤ 2, plot the x-intercept and draw a horizontal line through it. Shade the region below the line.
Step-by-step explanation:
To graph the inequality ½x - 1 ≤ 2, we can start by finding the x-intercept and y-intercept. The x-intercept is found by setting y = 0 and solving for x: ½x - 1 = 2 => ½x = 3 => x = 6. So the x-intercept is 6. The y-intercept is found by setting x = 0 and solving for y: ½(0) - 1 = 2 => -1 = 2, which is not true. So there is no y-intercept.
Next, we can plot the x-intercept (6) on the x-axis. Since there is no y-intercept, we can draw a horizontal line passing through the x-intercept. This line represents all the points that satisfy the equation ½x - 1 = 2.
Finally, we shade the region below the line. This represents all the points where ½x - 1 is less than or equal to 2.
The graph of the inequality ½x - 1 ≤ 2 is a horizontal line passing through the point (6, 0) with the region below shaded.