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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