Question

Write four linear inequalities that represents the following shaded region in the diagram

Answer 1

When the inequality is < or > you have a dotted line

When the inequality is ≥ or ≤ you have a full line

When the inequality is < or ≤ the shadow area is under the line

When the inequality is > or ≥ the shadow area is over the line

For the given diagram:

First line:

`y=0`

You have a full line and the shadow area is over the line, the inequality is:

`y\ge0`

Second line:

`y=-5x+5`

You have a full line and the shadow area is over the line, the inequality is:

`y\ge-5x+5`

Third line:

Find the equation:

- The liine goes througt point s(0,0) and (4,4)

Slope:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \\ m=(4-0)/(4-0)=(4)/(4) \\ \\ m=1 \end{gathered}`

y-intercept: value of y when x=0: y is 0 when x is 0

Equation of the line:

`\begin{gathered} y=mx+b \\ \\ y=x \end{gathered}`

You have a dotted line and the shadow area is under the line, the inequality is:

`yFourth line:[tex]y=6-x`

You have a dotted line and the shadow area is under the line, the inequality is

`y<6-x`Then, the four linear inequalities that represents the given diagram are:[tex]\begin{gathered} y\ge0 \\ y\ge-5x+5 \\ y