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in today's video we're looking at how to
find the equation of a line when you're
given that line on a graph like any of
these three
the key idea is that we can write
straight line equations in the form of y
equals mx plus c
where m is the gradient of the line
so how steep it is
and c is the y-intercept
which is the point where the line
crosses the y-axis
so all you need to do is find the
gradient and the y-intercept of a line
and plug those values into the equation
to see how this works let's start with
this question
where we need to find the equation of
the line on this graph
the easiest thing to spot is that the
line crosses the y-axis at y equals 2
which tells us that c must be 2.
the gradient though is a bit trickier
and there's a few different ways to find
it
but in this video we're going to use the
equation change in y
divided by change in x
which just means how much the y values
change by
divided by how much the x values change
by
so to use this we pick any two points
along the line for example these two
label them point one and point two
and then draw vertical and horizontal
arrows between them so that we can form
a right angled triangle
then to find our change in y we can see
that the vertical arrow goes from
positive five
all the way down to negative four
which is a change of minus nine
so our change in y is minus nine
in the same way the horizontal arrow
goes from x equals negative one
over to x equals two
which gives us a change in x of positive
three
this means that to find our gradient we
just do the change in y of minus nine
divided by the change in x of three
which will give us negative three
so m in our equation is minus three
and so to finish we just take our
equation y equals mx plus c
and plug in the minus 3 as m
and the 2 as c
which will give us y equals minus 3x
plus 2 as the equation of our line
before we finish let's try the same
thing for this one
the first thing you want to do with all
of these questions is write out y equals
mx plus c
because that's the general format that
we're going to try and put our equation
into
then to find c we need to look for the
y-intercept which is down here at
negative three
so you know that c is negative three
and next you need to find the gradient
which requires us to find the change in
y
and divide it by the change in x
so for that you need to pick two points
along the line
for example 0 negative three
and four negative two
label them both
and then draw the triangle thing
so if we go from point one to point two
and start with the y's
we can see that we've gone up by one
so our change in y is just one
and then if we look at the x values we
can see that we've gone along by four
so our change in x is four
this means that the gradient will be one
divided by four
which can't be simplified so m is just
one quarter
then to finish we just plug the c equals
negative three
and m equals a quarter
into our y equals mx plus c equation
to get a final answer of y equals one
quarter x minus three
anyway that's everything for this video
so hope it all made sense and cheers for
watching
