Answer:
[tex]\large\boxed{\left(-3,\ -\dfrac{1}{2}\right)}[/tex]
Step-by-step explanation:
Convert the inequality to the form y > mx + b:
[tex]-\dfrac{2}{3}x-4y>0[/tex] add 2/3x to both sides
[tex]-4y>\dfrac{2}{3}x[/tex] change the signs
[tex]4y<-\dfrac{2}{3}x[/tex] divide both sides by 4
[tex]y<-\dfrac{2}{(3)(4)}x[/tex]
[tex]y<-\dfrac{1}{6}x[/tex]
Put the coordinates of the points to the inequality and check:
for (-15, 3):
[tex]3<-\dfrac{1}{6}(-15)\to3<\dfrac{5}{2}\qquad FALSE[/tex]
for (6, 3):
[tex]3<-\dfrac{1}{6}(6)\to 3<-1\qquad FALSE[/tex]
for (-3, -1/2):
[tex]-\dfrac{1}{2}<-\dfrac{1}{6}(-3)\to-\dfrac{1}{2}<\dfrac{1}{2}\qquad TRUE[/tex]
for (6, -1/4):
[tex]-\dfrac{1}{4}<-\dfrac{1}{6}(6)\to-\dfrac{1}{4}<-1\qquad FALSE[/tex]
