Hey, guys.
Welcome to Algebra 1.
Today's lesson's going to focus
on finding X- and Y-intercepts
of linear functions.
Your knowledge
of evaluating expressions
in the coordinate plane
is going to come in handy
for this lesson.
You ready to get going?
Let's start.

(Describer) She uses a stylus on a screen.

Okay, before we start digging
into finding the X-
and Y-intercepts
of linear functions,
let's throw back
to graphing linear equations.
Here we have the graph
of Y equals 2X minus 1.
And knowing what we do
about relations in functions,
I know that I could apply
the vertical line test here
and that I could tell

(Describer) She draws a vertical line.

that this relation
is a function.

(Describer) Lines cross once.

Once I know that,
I can use what's called
function notation,
because now I know
that this relation
is a function of X.

(Describer) She writes.

For every input
there's only one output
for this relation, right?
Now I know
that it is a function.
Once I know that,
I can replace Y with F of X.
Let me erase
my vertical line here
so we don't get
too crowded, okay.
Once I know that my relation
is a function of X,
I can,
instead of using Y,
say that it's a function of X,
so that F of X
equals 2X minus 1.
That's how we read that,
"F of X,"
just shorthand
for "function of X."
Keep that in mind, and let's
look at this graph here.
Knowing what we do about
linear equations already,
I know how to investigate
and analyze this graph
and determine
where my X-intercept is
and where my Y-intercept is.
I know my Y-intercept
is the point
where my graph
crosses the Y-axis.
In this case, I'd have
a Y-intercept of negative 1.
I know my X-intercept's
where it crosses the X-axis.
In this case,
it appears to be half.
In this lesson we'll dig into
how to get to those values
just given algebraic
representation of a function,
so just given "F of X equals"
and then an expression.
Then we'll throw back
to the graphs
to make sure you get
the connection.
All right,
let's get going here.
So given, function of X,
or given F of X
equals 5X minus 15,
we're going to find the X-
and the Y-intercepts.
So we know, when we have
an X-intercept,
that our Y value is always 0.
Let's throw back
to that graph,
so I can show you
exactly what I mean.
So for this value here--
get the pen--
I know it's an X-intercept,
and that is the value
one-half, 0.
I know if I have
an X-intercept,
the Y value has to be 0
because I'm on the X-axis.
And my Y-intercept,
right here,
this one is at (0, negative 1).
That makes sense, because
any time I have a Y-intercept,
I know that the X value
has to be 0
because I'm on the Y-axis--
keep that in mind,
and we'll look back
at this problem.
Know that, if you have
an X-intercept--
I'll do a little
shorthand work over here--
for my X-intercept,
I know that my ordered pair
will always take the form
that there's some number for X,
but Y must be 0.
Then for my Y-intercept,
I know those ordered pairs
always take the form
that I have 0 for Y--
or 0 for X,
and my Y value
is some number,
but X has to be 0, right?
So we're going
to use that information
to find our X and Y intercepts
algebraically.
So first, let's get
the X-intercept.
Going to abbreviate that here.
For my X-intercept,
I know that Y must be 0.
Because we know that F of X
is another way to know
that that's Y--
when we see F of X,
we can just say,
"That's Y."
I'll replace F of X with 0.
I'm going to say
0 equals 5X minus 15,
because if I have
an X-intercept,
the Y value must be 0.
Then I'll just solve
this equation for X,
and I'll have the X value
for my X-intercept.
So let's get this solved.
We know we want
to isolate the X.
So let's start out by adding 15
to both sides.
So we know that's going
to cancel out there.
We'll have 15 equals 5X.
Let's scroll a bit,
get some more space.
We know our last step here
would be to divide by 5.
So 3 equals X.
That tells me
that my function
will cross the X-axis at 3.
I can represent this as
an ordered pair by saying,
well, then the X-intercept
is (3, 0).
That's the number,
that's the value of X
in this case, okay?
Let's scroll back up.
Now, to get my Y-intercept,
like we said, we know
that X has to be 0, right?
In this case, instead of
replacing F of X with 0,
we're going to replace
X with 0, all right?
Let me scroll down here
just to get some more space.
It's going to get
a little crowded
if I go right beside there.
All righty.
So we're going to find
our Y-intercept.
And we know that
our function was F of X
equals 5X minus 15.
And we know that
for our Y-intercept...
that we always have 0 for X,
and then some numerical value
for Y.
What we're going to do
to find our X-intercept--
sorry, our Y-intercept--
is replace X with a 0.
We're going to do
what's called find F of 0,
because we're going to replace
that X value with 0.
We'll say, all right.
Well, then 5 times 0
minus 15.
5 times 0, that's just 0.
So 0 minus 15,
which is negative 15.
So we know here
that our Y-intercept
is located
at (0, negative 15),
which we kind of probably knew
a little bit intuitively
because this is also an equation
written in slope
intercept form, right?
And we know
for slope intercept form,
that our Y-intercept
is always B--
or always that constant term
on the end, right?
You could also
look at it that way.
Just to get comfortable
with using function notation,
I'll substitute that value of 0
in there for X every time,
just to get comfortable
with that process,
because it'll be handy
a little later.
Let's move on
to another example.
Here we have the function,
one-third X plus 4.
And you want to find the X-
and Y-intercepts.
Okay, let's get
the X-intercept first.
Doesn't matter which one,
so I'll go in the order
that it was presented to me.
I always write down,
just to keep it straight.
I know that
for my X-intercepts
that I'll have
some value for X,
but that Y is always 0.
So if my function
is F of X equals
one-third X plus 4,
I need to replace
that F of X,
because I know
that it represents Y,
I want to replace that with 0.
So I will have 0 equals
one-third X plus 4.
Then I'm just going to solve
this equation for X.
Get a little more space.
So I'll subtract 4
from both sides, right?
So this is going
to cancel here.
Zero minus 4, that's negative 4
equals one-third X.
Let's get a little more
space here.
Now I need to get rid
of this fraction.
So I know I can multiply
both sides by 3.
3's will cancel there.
3 times negative 4,
that's negative 12 equals--
and then I'm just left
with 1X or just X.
I know here, my X-intercept
is at negative 12.
Or I could represent it

by the ordered pair
(negative 12, 0).
I know that that is the location
of my X-intercept, okay?
One thing's
checked off the list.
We found half of the problem
here, half of the answer.
Now let's turn and get
the Y-intercept.
And I may have given myself
enough space.
I don't want it
to get too crowded.
I'll come down
underneath here.
Okay, so now we'll find
the Y-intercept.
And we know
for the Y-intercept,
because I always like
to give myself a little hint,
I know that X
will always be 0,
but I'll have some
numerical value for Y.
Let's scroll back up
so we can get that function.
So our function of X
is F of X
equals one-third X plus 4.
So F of X equals
one-third X plus 4.
We know for Y-intercepts
that X is always 0,
so I'm going to replace the X
in my problem with 0.
I'll evaluate that
and see what I get there.
So F of 0 now--
because I'm replacing X with 0--
equals one-third
times 0 plus 4.
Let's get some more space.
Okay, we know that one-third
times 0 is just 0.
So that's 0 plus 4,
which is 4.
Which, like I said,
we knew that already,
because it's in slope
intercept form,
but there is a reason why
you should do this process.
It's going to come in handy
really soon down the line.
So I know that
my Y-intercept is at 4.
So I can write that
as an ordered pair (0, 4).
And there we go,
you're all done.
You've got both
your X-intercept
and your Y-intercept
for this function.
All right,
let's keep moving.
It is time for you to try one.
So press pause and work your way
through this problem.
Go ahead and find the X-
and Y-intercepts.
When you're ready
to check your answers,
press play.

(Describer) Titles: Given: f of x equals 8x minus 3.
Find the x and y intercepts.

(female narrator)
Given: F of X
equals 8X minus 3.
Find the X- and Y-intercepts.
Okay, let's see
how you did here.
Switch to my pointer tool
to reveal these answers.
So the X-intercept
for this function
is at 3/8ths, 0,
and the Y-intercept
for this function
was at (0, negative 3).
To see how I got that,
stay with me,
and I'll show you my work.
So first,
to find the X-intercept...
I'll write it
in the middle this time.
There we go.
I always make myself
a little note
that I know for my X-intercept
I have some value for X,
but Y is 0.
So I'm going to replace
F of X,
which I know is basically
like Y, with 0.
So 0 equals 8X minus 3.
Let's scroll down here.
Now I just need
to solve this equation.
I'll add 3 to both sides.
So that cancels out there.
And I have 3 equals 8X.
Scroll down
a little more.
Divide both sides by 8,
and you have
3/8ths equals X.
Then to write that
as a ordered pair,
you could write (3/8ths, 0).
Then you would have the location
of your X-intercept, okay?
Now, to get the Y-intercept,
we want to let X be 0,
right?
Let's get some room.
All right, so we're going
to get our Y-intercept now.
For the Y-intercept,
we know that X is always 0
and then Y
is some numerical value.
Let's scroll back up
to get that function.
So F of X equals 8X minus 3.
So F of X
equals 8X minus 3.
We're going to find F of 0,
because we're going to replace
that X with 0, okay?
So 8 times 0 minus 3.
8 times 0 is 0.
0 minus 3,
that's negative 3.
So the location
of our Y-intercept, here,
if I wrote it
as an ordered pair,
would be 0, negative 3.
All right,
good work there.
Let's keep moving.
We'll bring it back
to the graph
to make sure
you got that connection
between what you're doing
algebraically
and then what it looks like
on the coordinate plane, okay?
We know for X-intercepts,
that we--
it's easier to tell
on the coordinate plane
that your X is 0 because
you're looking for the point
where your graph is going
to cross the X-axis.
I see that point's right here.
I can say my X-intercept
is located at (2, 0).
I've got it that quickly.
I know for my Y-intercept,
I know that X is 0.
I'm looking for the point where
my graph crosses the Y-axis.
I'd look right here,
in this case.
It looks like I'm at one, two,
three, four, five, six.
One, two, three, yep.
So (0, negative 6).
And there's the location
of my Y-intercept, there.
So still a function,
but now we're looking at it
represented by its graph.
We can still get the X-
and the Y-intercepts.
Let's keep going.

(Describer) She switches to another graph.

Okay, so let's get the X-
and the Y-intercepts here.
So X-intercept,
looking for the point
where your graph crosses--
crosses the X-axis.
Here we go, right here.

And that is the location
(3, 0).
Y-intercept, I'm looking
for where my graph
crosses the Y-axis.
Let's see,
that's way up here.
One, two, three,
four, five,
six, seven, eight, nine.
So at--
get my pen here--
that's (0, 9).
There's our Y-intercept.
Then at (3, 0),
there was our X-intercept, okay?
All right,
let's keep moving.
It's time for you
to try one.
Press pause and take a minute
and locate the X-
and the Y-intercepts
of this linear function.
When you're ready to check
your answer, press play.

(Describer) The linear function crosses the x-axis at negative 2.
It crosses the y-axis at negative 8.

(female announcer)
The linear function
crosses the X axis
at negative 2.
It crosses the Y axis
at negative 8.
All right,
let's see how you did.
It looks like our X-intercept's
located right here...
and we are at (negative 2, 0).
Our Y-intercept--we're kind of
down low--let's count.
Negative 1,
two, three, four,
five, six, seven, eight.
So our Y-intercept
is at (0, negative 8).
Okay.
All right, good job on those.

(Describer) Next is a set of threee ordered pairs: 2, 28; 0, 14; and negative 2, 0.

(female announcer)
Next is a set
of three ordered pairs:

(2, 28), (0, 14),
and (negative 2, 0).
Now we're looking at--
again, we have a function--
but we're looking at it
by a list of some
of its ordered pairs.
We want to find,
what's our X-intercept,
what's our Y-intercept?
In this case,
it's important
that you remember
that shorthand little trick
I wrote down
that when you're looking
for your X-intercept,
you're looking for some
numerical value for X;
the Y must be 0, right?
And when you're looking
for your Y-intercept,
X must be 0
and you're looking
for some numerical value
for Y, right?
It looks like here,
I see I have (0, 14),
and I have (negative 2, 0).
So for my X-intercept,
I know Y has to be 0.
So there we go--
that's my X-intercept.
So my X-intercept
is at (negative 2, 0).
I know for my Y-intercept,
X must be 0.
So there we go,
our middle point, right there.
So for our Y-intercept,
it's located at (0, 14).
So it wasn't any work
as far as evaluating
an expression, and we weren't
on the coordinate plane.
We still needed to understand
that relationship with--
when I have an X-intercept--
you must remember Y is 0.
When you have
your Y-intercept,
you must remember
that X is 0.
Then once you're presented
with a list of points,
it's easy to locate
which is which.
Okay?
Let's keep moving.
This time we have
a list of four points,
but our process
is still the same.
They're asking us to find
the X- and Y-intercepts.
I know for my X-intercept--
I always start with this--
I know I need some numerical
value for X, but Y is 0.
For my Y-intercept,
I know that I need--
I know that I need some--
X is 0,
and I need some
numerical value for Y.

(Describer) The ordered pairs are 0, negative 3; 6, 0; 2, negative 2; and 8, 1.

(female narrator)
The ordered pairs
are (0, negative 3),

(6, 0), (2, negative 2),
and (8, 1).
So X-intercept,
I know Y's got to be 0,
so there we go.
It's my second point
listed here.
So X-intercept: (6, 0).
My Y-intercept,
I know that X must be 0
and I can look and see
it's the first point
listed here.
So Y-intercept is at 0,
negative 3.
All right?
Good job on that one.
It's time for you to try one
all on your own.
Press pause, take a minute
and try to locate
the X- and Y-intercepts
of this function.
When you're ready to check
your answer, press play.

(Describer) Title: Identify the x and y intercepts.
The ordered pairs are 2, 9; 3, 0; 5, negative 18; and 0, 27.

(female announcer)
Identify the X-
and Y-intercepts.

The ordered pairs are:
(2, 9), (3, 0),

(5, negative 18),
and (0, 27).
Identify the x-
and y-intercepts.
All right,
let's see how you did.
First, I'm writing
my little shorthand note.
X-intercept, X is some number,
Y has to be 0.
Y-intercept, X is 0,
Y is some number.
Now, don't think that
that number can't be 0, okay?
It can sometimes,
but you must remember
that for your Y-intercept,
X must be 0, okay?
The Y-intercept
could also be 0,
but the X has to be 0.
Then the reverse of that
for your X-intercepts, okay?
For my X-intercept,
I know I'm looking
for the point where Y is 0,
and it's here.
So my X-intercept is (3, 0).
My Y-intercept, I know
I'm looking for X to be 0,
and here we go.

It's that last point listed:
(0, 27).
All right.
Good job on that one.
We have reached the end
of our lesson, guys.
Great job solving problems
involving finding X- and Y-
intercepts of linear functions.
You saw how
all your prior knowledge
of algebra and pre-algebra,
the coordinate plane,
and evaluating expressions
all came together
to help you through this one.
See you soon
for more Algebra 1. Bye!

(Describer) Accessibility provided by the US Department of Education.