Answer:
No, it is not a good test point to choose since it's on the boundary.
(0,0) is a better choice
See graph below.
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Further Explanation:
The given point (-3,3) has x = -3 and y = 3 pair up together.
Plug those coordinates into the boundary line equation.
y = (4/3)*x + 7
3 = (4/3)*(-3) + 7
3 = -4 + 7
3 = 3
The fact we get a true statement at the end proves that (-3,3) is on the boundary line y = (-4/3)x+7
So the question is: which side of the boundary do we shade? The test point (-3,3) is literally on the fence, and it's indecisive on which side to pick. This is exactly why (-3,3) is a bad choice.
A better choice would be to use (0,0) since 0 is an easy number to work with and because the origin is not on the boundary line. See note below.
Let's plug x = 0 and y = 0 into the inequality.
y < (4/3)x + 7
0 < (4/3)*0 + 7
0 < 0 + 7
0 < 7
The last inequality is true, so (0,0) is in the shaded region. This means we shade everything below the dashed boundary line of y = (4/3)x+7 since (0,0) is below the boundary line.
The graph is shown below.
Side note: The origin is the first choice I'd go for as long as the origin point is not on the boundary. If it is on the boundary, then pick something else on the y axis such as (0,1) as a test point.