Need up to 30 seconds to load.

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