Question

Write the inequality shown by the Shaded region the graph which the body line Y equals 8X / 3 - 1

Answer 1

Equation of a shaded region

We have the body line described by the equation:

`y=-(8x)/(3)-1`

For the shaded region we have two possible cases:

`\begin{gathered} 1.\text{ }y\leq-(8x)/(3)-1 \\ 2.\text{ }y\ge-(8x)/(3)-1 \end{gathered}`

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:

`\begin{gathered} y??_{}-(8x)/(3)-1 \\ -3??_{}-(8\cdot(-3))/(3)-1 \\ -3??_{}8-1 \\ -3??_{}7 \end{gathered}`

Since -3 is minor than 7, the sign we use is ≤:

`-3\leq7`

Then, we have this time the case 1.

Answer: The inequality that describes the shaded region is y ≤ -8x/3 -1

`y\leq-(8x)/(3)-1`