ANSWER
[tex]y\text{ }\leq\text{ -}\frac{4}{3}x\text{ - 1}[/tex]
EXPLANATION
We want to write the inequality represented by the shaded region of the graph.
The boundary line of the graph is given as:
4x + 3y = -3
Let us put this in slope-intercept form:
=> 3y = -4x - 3
=> y = -(4/3)x - 1
Now that we have the equation in that form, we have to consider a few things:
=> The line used to represent the boundary line is a solid line. This means that the inequality we need has either a less than/equal to or a greater than/equal to sign.
=> The shaded region is on the left hand side of the boundary line. This means that the inequality represented is less than or equal to.
Therefore, the inequality represented by the shaded region is:
[tex]y\text{ }\leq\text{ -}\frac{4}{3}x\text{ - 1}[/tex]
