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in this video we're going to talk about
how to find the x and y-intercepts from
a graph and also from an equation and
also how to graph a linear equation in
standard form by using the X and y
intercepts so let's go ahead and begin
let's start with a graph
so based on this graph what are the x
and y intercepts the x intercept is
basically the x value where the graph
touches the x axis and it touches it at
an x value of 4 so that is the x
intercept you can write it as x equals 4
or you can write it as an ordered pair 4
comma 0 now what is the y intercept in
this particular graph all you need to do
is locate the Y value at which the graph
touches the y axis and that Y value is
negative 3 so I'm going to write it as 0
negative 3 as an ordered pair or you
could say y is equal to negative 3 so
that's how you can identify the x and y
intercepts from a graph now let's look
at another example so I'm going to draw
another graph and from it determine the
X and the y intercepts
let's do that again
so let's start with the x-intercept what
is the x-intercept in this problem so
notice that we have an x value of 3
that's where the curve intersects the x
axis so we have the point 3 comma 0
that's the x-intercept the y-intercept
occurs at a y-value of 2 that's where
the curve touches the y axis and so that
point is 0 comma 2 x is 0 but Y is 2 at
that point so now you know how to find
the x and y intercepts from a graph
that's all you need to do let's say if
you're given a linear equation y equals
2x plus 1 find the x and y intercepts
and then graph the function now
this linear equation is in slope
intercept form that is it's in y equals
MX plus B form M is the slope the slope
is the number in front of X so the slope
in this problem is 2 the y intercept is
B so we don't have to do anything to
solve for the Y know set so therefore we
have the point 0 comma 1 that's the
y-intercept but we need to do is find
the x-intercept in order to find the
x-intercept replace Y with 0 and find
the value of x to find the y-intercept
you can plug in 0 into X so for example
if you replace X with 0 you're going to
get y equals 1 which is always going to
be whatever this number is if it's in
slope intercept form but now let's go
ahead and calculate the x intercept so
let's subtract both sides by 1 negative
1 is equal to 2x and then let's divide
by 2 so the x intercept is negative 1/2
so it has a point it's negative 1 over 2
comma 0 now that we have the X and the y
intercept we can go ahead and make and
graph
so the y-intercept is at 0 1 and the
x-intercept is that negative 1/2 comma 0
which is about there approximately and
now we just got to make a line that
connects the two points and that's how
you can graph a linear equation given
the X and the y intercepts let's try
another example go ahead and graph the
equation 1/2 x - string by finding the x
and y intercepts so automatically we can
see the y intercept it's negative 3 so
we got the point is 0 negative 3 let's
find the x-intercept so let's replace Y
with 0 and let's calculate the value of
x so let's begin by adding 3 to both
sides negative 3 plus 3 is 0 so 3 is
equal to 1/2 X give it of the fraction
let's multiply both sides by 2 1/2 times
2 as a whole so on the right side all we
have left over is X 2 times 3 is 6
so therefore the x intercept is 6 comma
0 now that we have that we can go ahead
and make the graph
so let's plot the x-intercept first so
it's located at an x value of 6 but a
y-value of 0 and now let's plot the
y-intercept which is at 0 negative 3 and
then simply connect the two points with
a straight line and that's how you do it
now sometimes you might be given a
linear equation in standard form that is
in ax plus B y equals C form go ahead
and find the X and the y intercept to
find the x-intercept what you need to do
is replace Y with 0 now 3 times 0 is 0
and 0 basically is nothing so this
portion simply disappears so therefore 2
X is equal to 6 next we need to divide
both sides by 2 6 divided by 2 is 3 and
therefore this is the x-intercept so we
have the ordered pair 3 comma 0 now
let's find the y-intercept so this time
we're going to replace X with 0 so 2
times 0 is nothing so what we have left
over is negative 3y is equal to 6 so now
let's divide both sides by negative 3 6
divided by negative 3 is negative 2
so that's the y-intercept so now we have
the point 0 negative 2
you
now we can make the graph so let's start
with the x-intercept which is at an x
value of 3 on the x axis and then the
y-intercept which is at negative 2 on
the y axis and that's all you need to do
to graph that particular equation let's
work on one more example for the sake of
practice go ahead and graph this
equation so let's find the x-intercept
first so we're going to replace Y with 0
so we're going to have 3x is equal to 12
and 12 divided by 3 is 4 so the
x-intercept is 4 comma 0 next let's
replace X of 0 3 times 0 is 0 0 plus 4 y
is still 4y and then 12 divided by 4 is
3 so the y-intercept is 0 comma 3
now let's graph it so the first point is
that an X value of 4 and then the second
point is at a y value of 3 and then
simply connect the two points
and that's it so now you know how to
graph linear equations in Spanish form
and even in slope-intercept form there's
many different methods that you can use
but as you can see one method is simply
of finding the x and y-intercepts but
there's other methods out there so you
can check out the rest of the playlist
and find other videos on YouTube that I
have one graphing linear equations if
you want to know more now I want to show
you one of my algebra courses that might
be useful to you if you ever need it so
go to udemy.com
now in the search box just type in
algebra and it should come up so it's
the one with the image with the black
background so if you select that option
and if you decide to go to course
content you can see what's in this
particular course so the first section
basic arithmetic for those of you who
want to focus on addition subtraction
multiplication and division and it has a
video quiz at the end it's a multiple
choice video quiz you can cause it work
on the problems and see the solutions
they covers long division multiplying
two large numbers and things like that
the next tutorials on fractions add in
subtracting fractions multiplying
dividing fractions converting fractions
into decimals and so forth so you can
also take a look at that next solve the
linear equations which we covered and
just more examples if you need more help
with that the next topic order of
operations which is also useful graphing
linear equations you need to know how to
calculate the slope needs to be familiar
with the slope-intercept form standard
form and just how to tell if lines are
parallel perpendicular and so forth and
as a quiz that goes with that as well
the next topic is on
and absolute value expressions which are
also seen a typical algebra course and
then we have polynomials and that's a
long section and then factoring you just
that's not the topic you need to master
and then system of equations you can
solve it by elimination substitution
there's also word problems as well
sometimes you got to solve the equations
with three variables XY and Z so that
can be helpful
next quadratic equations how to use the
quadratic formula how to graph them how
to convert between standard and vertex
form and then you have rational
expressions and radical expressions
solving radical equations simplifying it
things like that and every section has a
quiz so you can always review what
you've learned if you have a test on X
day so here we have complex and magic
numbers you need to know how to simplify
those exponential functions logs I have
a lot of videos on logs and then this is
just functions in general the vertical
lines has horizontal line test had
itself or functions even or odd as an
conic sections graph in circles
hyperbolas ellipses parabolas things
like this too video quizzes because it's
actually a long section and finally
arithmetic and geometric sequences and
series so that's my algebra course if
you want to take a look at it and let me
know we think
