Answer:
y < -3 and
2x - 3y ≥ -15
Step-by-step explanation:
y < -3
Take any two points on the bold line
(0 , -5) and (-3 , -7)
Now find the slope for this line and then the equation of the line
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
[tex]= \frac{-7-[-5]}{-3-0}\\\\=\frac{-7+5}{-3}\\\\=\frac{-2}{-3}\\\\= \frac{2}{3}\\[/tex]
Slope, point equation,
y - y1 = m(x -x1)
[tex]y - [-5)=\frac{2}{3}(x-0)\\\\y +5 = \frac{2}{3}x\\\\3*y + 5*3 = \frac{2}{3}x*3\\\\3y + 15 =2x\\\\2x - 3y = -15\\[/tex]
Take any point from the shaded region and plugin the LHS of the equation.
(-6 , -5)
LHS = 2x - 3y
= 2*(-6) -3*(-5)
= -12 + 15
= 3 which is ≥ -15
2x - 3y ≥ -15
