Answer:
The answer is: y ≤ (2/3)x - 1/2
Explanation:
Add 2y to both sides of the inequality:
2/3x ≥ 1 + 2y
Subtract 1 from both sides of the inequality:
2/3x - 1 ≥ 2y
Divide both sides by 2 to isolate y:
y ≤ 1/2(2/3x - 1)
This gives you the inequality in slope-intercept form, y ≤ (2/3)x - 1/2, where the slope is 2/3 and the y-intercept is -1/2.
To graph the boundary line, plot the y-intercept at (0, -1/2) and then use the slope to find another point. For example, if you move up 2 units and to the right 3 units from the y-intercept, you'll arrive at the point (3, 1/2). Connect these two points with a straight line to graph the boundary line.
Finally, to shade the region of the coordinate plane that satisfies the inequality, test any point above or below the boundary line to see if it's a solution to the inequality. If the point satisfies the inequality, shade the region that it's in. If it doesn't, shade the opposite region.