Graphing Linear Inequalities in 2 Variables Video Lecture - Class 11

hello this is mr. T with a tutorial on
graphing linear inequalities the graph
of a linear inequality comprises two
parts we have a boundary line which is
either graphed as a solid line or a
dotted line depending on whether the
line is part of the solution and then a
shaded part of the graph on linear
inequalities all of the solutions will
fall on one side of the line and the
other side of the line will contain all
of the false parts the coming slides
will talk about how you decide which
part to shade if we look at this next
example we have this inequality 5x minus
2y greater than 10 our first part is to
be able to graph the equation 5x minus
2y equals 10 to find the boundary line
since this equation is in standard form
the quickest way to do that would be to
use the hide-and-seek method if I hide
the minus 2y I get my x-intercept of 2
and if I hide the 5x I get my
y-intercept of negative 5 since this is
a strictly greater than we're going to
use a dotted line so let's graph the
line using the Y x and y intercepts and
make the dotted line now we have to
decide which side to shade to do that
we're going to use a test point if you
need to pick a point that's not on the
line if 0 0 is not on the line that's
going to be the easiest problem easiest
point to calculate with if we put 0 0
into the inequality we get 0 greater
than 10 which is false that means that
all the points on the side of the line
where the test point is make it false
therefore the other side has the true so
we want to shade the side that's true so
we shade this other side
that can be you know making the test
point can be a little bit time-consuming
so there is a shortcut we can use if we
solve the inequality first for y so we
get Y by itself on the Left we can then
use the inequality symbol to know
whether to shade below the line if it's
a less than or above the line if it's
greater than if you're not sure you can
always pick a test point to check your
solution so we look at another example
if we do this one and the quick way we
have to first solve this equation for y
remember since I had to divide by a
negative I had to flip the inequality we
use the slope intercept form to graph
the line so the y-intercept is at
negative 3 and the slope is 2 so we go
up 2 over 1 and this time since we have
the equals part we draw a solid line
since this is a less than we have to
look where we have the Y by itself that
means we want to shade below you can put
your pencil on the line and go straight
down to find where below is sometimes
when the graphs is very steep it's not
obvious which ways up or down again
these graphs show that the shaded side
all the points over here make this
original inequality true and all the
points over here make it false hope this
helps you