Often times it�s better to write the equation of a line in one format or another for various
reasons and that format we call a form and there is a few different forms of a line there
is slope intercept form there is point slope form and the last common one is this one called
standard form that is what we are going to talk about in this video so standard form
looks like this you have got capital a, x plus capital b, y equals capital c or capital
a b and c will be numerical values so for example an equation in standard form might
look like this you might have 2x minus 3y equals 5 so that a is 2 the b is negative
3 and the c is 5 and this linear equation is written in what we call standard form,
alright now let�s take a look at these 2 real quick here to see if you can identify
which if any or both of these are in standard form this one is in standard form because
it looks like a, x plus b, y equals c but notice this one over here the x and the y
are not on the same side, the y is on one side and the x is on the other side with a
constant so this would not be in standard form now even if an equation is not written
in standard form you can actually write it in standard form by moving some terms around
now this one if we didn�t give up on it we could probably add x to both sides you
will notice and once the x is cancelled then you will x plus y equals 7 and then now it
is in standard form again cause we have 1x plus 1y equals 7 so you can put equations
in standard form if they are not already in standard form but the original one was not
but the new one is in standard form alright now where why might we use standard form like
does it have any special use or do we see it for a particular reason and the answer
is yes we often see standard form when we are trying to find x and y intercepts a lot
of the problems a lot of the equations will be provided in standard form and here�s
why if your equation is in standard form if you are looking for the x intercept how do
we do that well as you well know we let the y be 0 that�s how we find an x intercept
and if you let the y be zero and you are in standard form, bam you can immediately solve
for x in 1 step because you just have a, x equals c and likewise if you are trying to
find a y intercept and as you well know we will let the x coordinate be zero to find
a y intercept it�s the same deal you let the x be zero and it goes away and we are
one step away automatically from finding the y intercept if it was in one of these forms
like point slope form or slope intercept form you will have a lot of additional steps but
it�s very very quick when its written in standard form so you will notice if you look
throughout your text book the section on finding x and y intercepts the equations that they
give you will be littered with these equations written in standard form so let�s try one
let�s see if this is actually any good so here is a linear equation 3x minus y equals
6 and let�s see if we can find the x and the y intercept and see how easy that is so
for the x intercept we know we are going to let the y coordinate be 0 so we will have
3x equals 6 because the y goes away and automatically we have it we divide by 3 and x equals 2 there
is your x intercept x intercept is at the point 2 comma zero very very fast and the
y intercept on the other hand was three times zero minus y equals six so 3 times 0 is 0,
0 minus y is negative y equals 6 and again automatically we have it y is equal to negative
6 so we will have a y intercept comma negative 6 so it�s very very fast to find x and y
intercepts when its written as a, x plus b, y equal your constants on the opposite side
alright now just in closing I just want to convince you that we did do this correctly
here is our x and y intercept x intercepted 2 and y intercept at negative 6 and I went
ahead and graphed this linear equation and sure enough look we are absolutely dead on
and it was so so so fast to find these x and y intercepts but we found them most easily
because the equation was written in standard form.