Question

How do I know when to plot the inequality going up or down and can you check if what I put is right?

Answer 1

Given the inequality:

`y\ge x-4`

You can identify that the boundary line of the inequality is:

`y=x-4`

Notice that it is written in Slope-Intercept Form:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

In this case, you can identify that the y-intercept is:

`b=-4`

In order to graph the line, you can find the x-intercept by substituting this value of "y" into the equation and solving for "x":

`y=0`

Because the value of "y" is zero when the line intersects the x-axis.

Then, you get:

`\begin{gathered} 0=x-4 \\ x=4 \end{gathered}`

Now you know that the line passes through these points:

`(0,-4),(4,0)`

Notice that the symbol of the inequality is:

`\ge`

That indicates that the line must be solid, and the shaded region must be above the line.

Knowing all that information, you can graph the inequality.

Hence, the answer is: