Question

Y+5<-x how do I do this

Answer 1

First step is to change the symbol < to = sign.

`\begin{gathered} y+5<-x \\ y+5=-x \end{gathered}`

Get the x and y intercepts

For x intercept, set y = 0

`\begin{gathered} 0+5=-x \\ x=-5 \end{gathered}`

For y intercept, set x = 0

`\begin{gathered} y+5=0 \\ y=-5 \end{gathered}`

Now we have the points (-5, 0) and (0, -5)

Plot the points and connect it with a dashed line.

Note that dashed line is used if the symbol is < or >

Solid line is used if the symbol is ≥ or ≤.

Next is to determine which region needs to be shaded.

Test the inequality with (0, 0)

If the inequality is TRUE, (0, 0) is included in the region.

If the inequality is FALSE, (0, 0) is NOT included in the region.

Substitute (0, 0) to the inequality :

`\begin{gathered} y+5<-x \\ 0+5<-0 \\ 5<0 \end{gathered}`

Since the inequality is FALSE, (0, 0) is NOT included in the shaded region.

From the graph, the shaded region must be B