All language subtitles for English (auto-generated)_en_0_Graphing Lines in Standard Form (ax by _ c)(1080P_HD)

professor Dave again let's graph some

more lines we now understand how to

graph lines in the coordinate plane but

we have been doing this exclusively

using the y equals MX plus B form

otherwise known as the slope-intercept

form

there is another form that we will see

for lines and it's called the standard

form which is ax plus B y equals C this

is just another way of communicating

linear relationships and it can be

useful in certain situations especially

if we want to graph a line very quickly

to see why it's so easy to graph this

way let's try an example say we have 4x

plus 6y equals 12 instead of plugging in

x values to make a table let's just

rationalize that the y-intercept or the

point where the line crosses the y-axis

must have an x value of 0 likewise the x

intercept or the point where the line

crosses the x axis must have a y-value

of 0 for this reason to find the y

intercept we can just plug in 0 for X

the X term will go away 6y equals 12 so

y equals 2 that means the y intercept is

the point 0 2 then to find the x

intercept we plug in 0 for y the y term

will go away 4x equals 12 and x equals 3

that means the x intercept is the point

3 0 with two points on the line now a

parent we are ready to draw the line and

that's all there is to it so we should

note that standard form is useful when

trying to find the intercepts of a line

and when trying to quickly graph the

line however if we want to talk about

the slope of the line it's a little

trickier and slope intercept form is

better for that

since the slope is listed right in the

equation if we have a line in standard

form and we want to know the slope there

are two things we

we could take the two intercepts which

represent points on the line and use the

coordinates of those points to calculate

the slope for this example the two

points are 0 2 & 3 0 that means the rise

is negative 2 and the run is 3 which

gives us negative 2/3 for the slope the

other thing we could do is convert this

equation into slope-intercept form all

we have to do is solve for y so the

first thing to do would be to subtract

4x from both sides now we have 6y equals

negative 4x plus 12 then we divide both

sides by 6 that gives us y equals

negative 4 sixths X which simplifies to

negative 2/3 X plus 12 over 6 which is 2

and converting from standard form to

slope-intercept form is just that simple

we could also go in Reverse from slope

intercept to standard form to do this we

should note that in standard form a B

and C must be integers

they can't be fractions so the first

thing we would do is multiply everything

by 3 that gives us 3y equals negative 2x

plus 6 then we could add 2x to both

sides to get 2x plus 3y equals 6 now we

can see that this form is actually a

little simpler than our original

equation in fact each term seems to be

half of the original term what this

tells us is that when writing an

equation in standard form not only do a

B and C have to be integers but they

should be in the lowest ratio of these

integers that is possible 4 6 and 12 can

all be divided by 2 to get a simpler

version of the equation so this will be

the more correct version of the equation

we would still get the same values for

the intercepts and therefore the same

line but we always want the simplest

form of the equation possible so we must

bear this in mind when converting

between the two linear forms

now that we have both of these forms

down let's check comprehension thanks

[Music]

[Music]

for watching guys subscribe to my

channel for more tutorials support me on

patreon so I can keep making content and

as always feel free to email me

professor Dave explains at gmail.com

[Music]