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Studying for a test? Prepare with these 17 lessons on Solving basic equations & inequalities (one variable, linear).

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# Solving and graphing linear inequalities

Video transcript

We're asked to represent the
inequality y is greater than 5 on a number line and on
the coordinate plane. Let's do the number
line first. Let me just draw out
a number line. That's my number line, all
the possible values of y. Let's make that 0 on
the number line. We could obviously go into
negative numbers, but we're going to be greater than
5, so I'll focus on the positive side. So let's say that's 1, 2, 3,
4, 5, and then 6, 7, so forth and so on. This number line represents y,
and y is going to be greater than 5, not greater
than or equal to. So we're not going to be
including 5 in the numbers that can be y. So we're not going to include
5, so we're going to do an open circle around 5, and all
of the other values greater than 5 will be included. So if there was a greater than
or equal to sign, we would have filled it in, but since
it's just greater than, we're not including the 5. So we've represented it
on the number line. Let's do the same thing on
the coordinate plane. Let me draw a coordinate
plane here. I'm just using the standard
convention. That is my y-axis right there. And then the horizontal axis,
I'll just assume is my x-axis. Let me draw some y values,
positive y values. 1, 2, 3, 4, 5. That is 5 right there, and you
go 6, 7, you can just keep going into larger and
larger numbers. And we want y to be greater than
5, so it's not going to be greater than or equal to. So we're not going
to include 5. So at 5, at y is equal to 5,
we will draw a dotted line. That shows that we're not
including y is equal to 5, but we want include all of the other
values greater than 5. So that we will shade in. So here we have shaded in all of
the values greater than 5. If it was greater than or equal
to 5, we would have drawn a bold line over here. So no matter what x is, no
matter what x we pick, y is going to be greater than 5.