Equation of a shaded region
We have the body line described by the equation:
[tex]y=-\frac{8x}{3}-1[/tex]
For the shaded region we have two possible cases:
[tex]\begin{gathered} 1.\text{ }y\leq-\frac{8x}{3}-1 \\ 2.\text{ }y\ge-\frac{8x}{3}-1 \end{gathered}[/tex]
We select any point from the shaded region. This time we are going to work with the point (-3, -3), that is when x = -3 and y = -3.
We are going to replace it in the equation and after that we are going to complete it using one of the signs ≥ or ≤ using the one that gives as a true inequality:
[tex]\begin{gathered} y??_{}-\frac{8x}{3}-1 \\ -3??_{}-\frac{8\cdot(-3)}{3}-1 \\ -3??_{}8-1 \\ -3??_{}7 \end{gathered}[/tex]
Since -3 is minor than 7, the sign we use is ≤:
[tex]-3\leq7[/tex]
Then, we have this time the case 1.
Answer: The inequality that describes the shaded region is y ≤ -8x/3 -1
[tex]y\leq-\frac{8x}{3}-1[/tex]
