Examples: Graph of a linear equation Video Lecture | Quantitative Aptitude for Competitive Exams - SSC MTS / SSC GD

hello friends this video on linear
equation in two variables part 6 is
brought to you by exam viacom no more
here from exam let us take one more
example you know that in fact you will
study all these things physics that's
what I was telling that this chapter has
application in physics as then so we
know that force applied on the body this
guy is applying force in the body on the
body and this is the body disposal of
some mass the force is directly
proportional to the acceleration of the
body this body will accelerate and so
the force is directly proportional to
acceleration okay write the equation to
express this situation and plot in the
Klan so the equation will be if my force
is y an acceleration is X and since it
is proportional I can say that some
constant into acceleration right so you
can write this equation as Y is equal to
K into X where K is any constant but to
plot this graph plot this line in the
graph I had to have some value constant
and it says you know constant is 5 I can
have any value I can assume K to be 3
into before I assume K is equal to find
my equation is y is equal to 5x because
to draw the graph I need the actual
equation right I could draw graphs with
the constant Y is equal to 5x is the
equation I have so let's get some point
here so if X is equal to 0 Y is what Y
is also 0 that is one point let's take
another point let us take X is equal to
1 so if you put X equal to 1 Y is what I
win 2-1 that is right so I have two
points right so X is going to 0 Y is 0 X
is equal to 1 Y is 5 2 points I have so
X going to 0 Y is going to 0 at this
point X is equal to 1 Y is going to find
this
so I had these two points enjoying these
two going to actually again draw the
graph this has to be straight line it is
not here
at any point on these line is the
solution for example if you want to find
X is equal to let's suppose minus 1 what
is the value of y so it's equal to minus
1 like like there is in DC which is here
and this is minus 1 comma minus 5 so X
going to minus 1 Y has to be minus 5 and
we can actually cross check that Y is
equal to 5 into minus 1 is minus 5 ok so
if you see this is the graph y is equal
to 5 X this is the kind of graph you get
and you get as well graph or Y is equal
to 3 X 2 X because the value of constant
is not given okay
so if you see this cushion and the sword
using equations linear equation in two
variables let's take a similar question
get the two equation of lines passing
through 2 comma 4 T so many equation I
can have if I say X plus y just express
by a form this is to this protein this
comes out to be 16 so one equation will
be X plus 2 y is ready section if I
write equation in the form of 2 X plus y
I put X square root 2 and this is 14 2
into 2 is 4 4 plus 14 is 18 this is
another equation if I say let's suppose
3x plus y let's put the value 2 and 14 3
into 2 is 6 6 plus 14 is 20 this is
another equation if I say X minus y
would do it is 14 here too - footings -
12
this is another equation so I can have
so many equations just write any
amplifier loop 3x plus 5y or something
anywhere where I put the value put any
abrupt X&Y
expression put the value of x + y
is given this to end is 14 so already
this is 14 by 70 70 plus 676 so this is
the equation you have infinite number of
equation since they are infinite number
equations there are infinite number of
lines that will pass to a point and that
is true if you have a point now infinite
number of lines passing to that one okay
the question says that if point three
comma four lies on the graph of this
equation find the Matt ok there is the
equation this is the graph and there is
some line and this equation line of the
line is 3 y is equal to ax plus 7 and it
says that 3 comma 4 is actually levi's
for this body so 3 comma 4 is actually
solution to this line 3 comma 4 lies on
this graph right so you 3 comma 4 lies
on the graph of this equation that means
3 comma 4 is solution for linear
equation this correct statement is the
point 3 comma of hole lies in the graph
of the equation some equation that means
3 comma 4 the solution for this equation
let us put the value of 3 comma 4 in
this equation 3 y is 4 is equal to a X
is 3 plus 7 so let us stop 12 is equal
to 3a plus 7 or 3 is equal to 12 minus 7
or E is equal to 2 and minus 7 is 5 5 by
3 and that is matched pretty easy so if
a point lies on the graph of a equation
that means the point is the solution for
the equation that is something should
know let's take one more application in
the world done by a body on a
application of the constant force is
directly proportional to this is tired
so this guy is applying some force and
the work done is directly proportional
to distance traveled so let's suppose it
traveled from here to here
this is the distance travel to blisters
express this in the form of equation in
two variables so let us assume work done
is y and this is to ever this legs okay
and there is a constant so I can say
that Y is equal to some constant into X
so this will be the equation and this is
the equation of two variables if you see
okay constant force is given five
minutes okay is five that is given so Y
is equal to five x please note in the
earlier example the constant value was
not given so we have assumed it to be
five could have assumed any value but in
this scale the constant value is given
this five minutes okay because the
actual form line physics if you learn is
work is but new force into distance okay
this is the actual formula this is
values given this is when you in this
case so Y is equal to five x in the
graph you get and we have to plot does
okay so why will the five x is something
we should have plotted so let's first
plot two points so Y is equal to 5x
let's take X equal to zero you take X
equal to zero Y becomes zero that is one
fine you take X equal to 1 taking X
equal to 1 Y becomes 5 into 1 that is 5
that is only point we have to point in
plot X is equal to 0 Y is producer is 1
point X equal to 1 y is greater than 5
is another point is here so with this
actually you can draw a line okay this
is the graph y and this is the graph
corresponds to y is equal to X now the
question is what is the ball then when
distance by the body when the distance
travel is 2 units so we expand is
actually go to image when I go and have
the space but actually again for on this
equation y is equal to 5 X X is equal to
2 so you get 10 so the work that is 10
units the next is 0 in it for 0 unit you
can actually see the graph this point is
0 comma 0 for X equal to 0 Y is 0
indirectly say the work done is zero
units already can actually form the from
the equation y is equal to 5x put X
equal to 0-5 in Brazil to 0 you can see
that the RISM the matching calculate or
just photographed looking at the graph
you can see so in the scale so if we had
the graph we extend is actually
somewhere so you see that for point two
it will hit this point and this point
will actually be to order you can try
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