How do you graph the inequality #x-2y>=-7#?

To graph the inequality x - 2y ≥ -7, follow these steps:

1. Begin by graphing the boundary line, which is the equation x - 2y = -7. To do this, first rewrite the equation in slope-intercept form (y = mx + b): x - 2y = -7 -2y = -x - 7 y = (1/2)x + 7/2

2. Plot the y-intercept, which is (0, 7/2), and use the slope (1/2) to find another point. For example, move one unit to the right (increase x by 2) and two units up (increase y by 1), giving the point (2, 4).

3. Draw a dashed line through these two points. Because the inequality is ≥ (greater than or equal to), the boundary line should be drawn as a solid line.

4. Determine which side of the boundary line to shade by testing a point not on the line. A convenient point to test is the origin (0,0). Substitute the coordinates into the original inequality: x - 2y ≥ -7 0 - 2(0) ≥ -7 0 ≥ -7

   Since 0 ≥ -7 is true, shade the side of the line containing the origin.

5. Finally, label the shaded region to indicate that it represents the solution to the inequality.

6. If needed, you can also label the boundary line for clarity.