For the following linear inequalities draw the feasibile region
i: x _>1
ii: x+y _<2
iii: x-axis
To draw the feasible region for each of the given linear inequalities, we need to plot the graphs of these inequalities on a coordinate plane. Let's go through each inequality one by one.
i) x ≥ 1:
To graph this inequality, we draw a vertical line passing through the x-coordinate 1. Since the inequality includes the equal sign (≥), the line should be solid. Shade the region to the right of the line because x is greater than or equal to 1.
ii) x + y < 2:
To graph this inequality, we need to rewrite it in slope-intercept form (y = mx + b). Rearranging the inequality, we get y < -x + 2. The inequality does not include the equal sign, so the line should be dashed. Draw the line y = -x + 2. Shade the region below the line because the inequality states that y is less than (-x + 2).
iii) x-axis:
The x-axis is a horizontal line that lies on the x-coordinate plane. Since there is no inequality given for this part, the feasible region is the entire x-axis.
Once we have graphed each inequality, we can find the intersection of all the shaded regions. This intersection represents the feasible region for the given system of inequalities.