Kyle determines that y ≥ − 8/3 x-4 is shown on the graph. Is Kyle correct? If not, determine the correct inequality.
A) Yes, Kyle is correct.
B) No, Kyle is incorrect. The correct inequality is y < − 8/3 x+4
C) No, Kyle is incorrect. The correct inequality is y > − 8/3x-4
D) No, Kyle is incorrect. The correct inequality is y ≤ − 8/3 x-4

This graph has a dashed line, so it would be either less than or greater than. The only way to find out is to use the zero-interval test [test point (0, 0)] to ensure whether we share the opposite portion [the portion that does not contain the origin] or the portion that DOES contain the origin. This is where we verify the inequality as false or true:

Greater than

[tex]\displaystyle 0 > -\frac{8}{3} - 4 → 0 > -4[/tex]☑

Less than

[tex]\displaystyle 0 < -\frac{8}{3} - 4 → 0 ≮ -4[/tex]

This graph is shaded in the portion of the origin, so we choose the greater than inequality statement.

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