Substitute the coordinates of each point into the expression on the left hand side of the equation to find which of them make the expression to be equal to 4.
[tex]\frac{2}{3}x-\frac{1}{2}y[/tex]
A (3,8)
Substitute x=3 and y=8:
[tex]\frac{2}{3}(3)-\frac{1}{2}(8)=2-4=-2[/tex]
B (0,8)
Substitute x=0 and y=8:
[tex]\frac{2}{3}(0)-\frac{1}{2}(8)=0-4=-4[/tex]
C (2,5)
Substitute x=2 and y=5:
[tex]\frac{2}{3}(2)-\frac{1}{2}(5)=\frac{4}{3}-\frac{5}{2}=-\frac{7}{6}[/tex]
D (6,0)
Substitute x=6 and y=0:
[tex]\frac{2}{3}(6)-\frac{1}{2}(0)=\frac{12}{3}-0=4[/tex]
Therefore, the point (6,0) is a solution to the given equation (option D).
