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:

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{4-0}{4-0}=\frac{4}{4} \\ \\ m=1 \end{gathered}$

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