The system of inequalities y≥−4x−4
and y≤12x
is graphed. Which region is the feasible region (solution)?
To graph the system of inequalities, let's start by graphing each inequality separately:
1) y ≥ -4x - 4:
Plot the y-intercept at -4 and use the slope of -4 to find additional points. We connect the points with a solid line because the inequality includes y ≥ -4x - 4.
2) y ≤ 12x:
Plot the y-intercept at 0 and use the slope of 12 to find additional points. We connect the points with a dashed line because the inequality includes y ≤ 12x.
Now, let's shade the feasible region. Since we have a "y ≥" inequality, we shade above the solid line for the first inequality. For the second inequality, we shade below the dashed line since it is "y ≤".
The feasible region is the shaded area above the solid line and below the dashed line.