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: