How do you graph Y=[x]-5 and y>[x]?

Answer 1

Graph the line y = x - 5 (slope=1, y-intecept=-5)
Now graph the line y = x. You'll see if you shade everything above this second line (y > x), it doesn't intersect with your first line.

So the answer is the null set (no graph)

Another way to see this is to solve for x:
x = y + 5

Now plut this into your second equation:
y > y + 5

There is no solution for this...

Edit: I reread your question and realized your [ x ] notation was intended to mean absolute value. I would have written it | x |. However, it doesn't make a difference.

For negative x values, you have x < 0. This makes lines with negative slopes, but even when they flip slopes, the y > -x line will be above the y = -x - 5 line.

For the negative values of x (x < 0), you have:
y = -x - 5
y > -x

The first line has a slope of -1 and an intercept of -5.
Again if you solve for x:
x = -y -5
-x = y + 5

Plug it into the inequality:
y > y + 5

Again, no solution.

So the correct answer is an empty graph...

Answer 2

It depends. If you know how to graph slope intercepts
then just graph it in slope intercept form. But since it has absolute values then x could be both positive and negative and so you should reflect the line to the left. And the second one is the same thing but if y is greater than then you should shade in the right side of the line. And since the sign is greater than and not greater than and equal to then the line you draw should be dotted. I hope this was a good explanation. If not you can email me.

Answer 3

Y = [x] - 5 plots as a "stairstep" starting at (0,-5) with a rise of 1 and a tread of 1
y > [x] also plots as a "stairstep", but starting at (0,0).use a dotted line for this plot, and shade above it to indicate the inequality.