Question

To graph the inequality -4 ≥ w, you would put a closed circle on -4 and shade to the right.

Answer 1

how it works:
Think about how you've done linear inequalites on the number line. For instance, they'd ask you to graph something like x > 2. How did you do it? You would draw your number line, find the "equals" part (in this case, x = 2), mark this point with the appropriate notation (an open dot or a parenthesis, indicating that the point x = 2 wasn't included in the solution), and then you'd shade everything to the right, because "greater than" meant "everything off to the right". The steps for graphing two-variable linear inequalities are very much the same.

Graph the solution to y < 2x + 3.
Just as for number-line inequalities, my first step is to find the "equals" part. For two-variable linear inequalities, the "equals" part is the graph of the straight line; in this case, that means the "equals" part is the line y = 2x + 3:



Now we're at the point where your book probably gets complicated, with talk of "test points" and such. But when you did those one-variable inequalities (like x < 3), you didn't bother with "test points"; you just shaded one side or the other. We can do the same here. Ignore the "test point" stuff, and look at the original inequality: y < 2x + 3.

I've already graphed the "or equal to" part (it's just the line); now I'm ready to do the "y less than" part. In other words, this is where I need to shade one side of the line or the other. Now think about it: If I need y LESS THAN the line, do I want ABOVE the line, or BELOW? Naturally, I want below the line. So I shade it in: