hello everyone in this lesson i'm going to show you how to draw a straight line there are two main methods i'm going to start off with the table method so as the name suggests we will need a table you then need x and y you will then choose three points so for example you could choose -2 as your x 0 as your x and 2 as your x you then plug those values into this equation to find the matching y value so for example for the first x value you could choose you chose minus two and you can choose whatever you like by the way it's just nice to choose something negative then a zero and then something positive but you could have chosen minus three zero and three or minus one zero and one it's up to you now if you have to go type this in on the calculator you are going to end up with zero okay so we just fold that in on the table then we move on to the next point so x is now zero so we say y equals to two brackets zero plus 4 and that would give you a y value of 4. you then plug in 2 so that would be y is equal to 2 times 2 plus 4 and that's going to give you a y value of 8. we can now draw the graph okay so always remember that x is on the horizontal and then y is on the vertical so the first point is minus two and zero so it's x value of minus two but a y value of zero so it's literally on that line then we've got a the second point is zero and four so the x is zero meaning we're not going to go left or right but we're gonna go straight up to four so there we have it then the last point is 2 and 8. so 2 on the x so there we go and then 8 on the y so up to there and then we put a little dot and there we have it we then put a line right through those dots and there you have yourselves a straight line so that is called the table method now a different way to do it is to use the intercept method let me show you that so intercept method you got to think about what that means intercept is the places where the line cuts the y and where it cuts the x-axis so we are going to find the intercepts so we're going to find two points okay and we don't know where they are but i'm going to show you how to find them so let's think about the x-axis for now if we want to know where does that line go through the x-axis maybe the line looks like this then it would be over there maybe the line does this then it would be over there to find that out we're going to do the following on this line that i'm showing you now the x-axis the y-values are always zero so what we do is we go to our equation and we make the y value 0 and then we simply do this and then you solve this equation to find x so to find the x intercept we make y 0. i'm just going to summarize that here to find x intercept you make y equal to zero okay so now if we go solve this we know that this plus four we can take it to the left or there's various ways to do this i'm just trying to keep this 2x positive so we're going to end up with 2x equals to negative 4. to get x alone you then divide both sides by 2 and so x is going to equal minus 2. so we knew that we were somewhere on this line over here but where specifically where x is minus 2. so now we can put a dot over there now we're going to work on this line and we're going to find the intercept there on that line x is always zero so to find the y-intercept we will make x equal to zero so we go to our equation and we make x equal to zero so y equals to two zero for x and if you go to work that out you're going to get 4. so we knew we were somewhere on this line over here but we didn't know exactly where but now we know that we are at the place where y is equal to 4. and there we have our two points and you actually only need two points to draw a straight line and so there we have it okay so we have two methods table method and intercept method with the table method you should find you could find two points in the table method as well but many teachers will tell you to find three then for the intercept method which is the one we've just done now you only find two points you find the x-intercept by making y zero then you find the y-intercept by making x equal to zero just remember that to find the y-intercept you make x zero and to find the x-intercept you make y zero all right so to end of this lesson we are going to practice both methods we are going to draw the line y equals to 3x minus 6 using the table method and the intercept method with the table method let's just use two points i know many teachers want you to use three but you only need two points it's just gonna save you time all right so we draw ourselves a table and then the trick is to choose two points that are one is negative so for example minus two and the other one's positive so what we do is we plug those x values into the equation so to get the y values so it will be y equals to 3 bracket minus 2 minus 6 and that's going to give us a y value of -12 so we fill in y value of minus 12. we then do the same with this x value so that will become y equals to three two minus six and that's going to give us six minus six which is zero and so now we have two points we've got the point minus -2 that goes with -12 and then we've also got the point 2 that goes with 0 and so we can put those on our graph so i'm just going to do a rough sketch graph and i'm not going to go label it minus 2 minus 12. it's going to take a long time but minus 2 would be somewhere to the left and then minus 12 would be somewhere down here so the line is going to be approximately over there then at the point 2 and 0 2 on the x would be somewhere over here and then 0 on the y so it's a dot that's on the x axis and let me just label that minus 2 and minus 12 2 and 0. you can then draw your line and there is our line now we use the intercept method and so we need to find the x-intercept to do that you make y equal to zero so you let me just write down this equation and so we make y equal to zero and then you solve for x so you can take the minus six over so it becomes positive you then divide both sides by three and so x is two so when y is zero x is two so we can say that when y is zero x is two so there's our point see how we've got the y value equal to zero okay and then we need to find our y-intercept to do that we make x equal to zero so we take the equation and we make x equal to zero and so that's going to be minus six so when x is zero then y is minus six and so there we have a point and there we have a point so now we can draw a graph so if we go to this point first x is two and then the y is zero so it's on the line the intercepts are always on the line and then with this one your x is zero but your y is minus six so it just goes down over there and then you can put a line through that and then always label your points so that'll be two zero and zero and minus six and so yes the numbers on the graphs are going to be different but i promise you they are actually the same line and there you have it guys you've got the table method and the intercept method thanks for watching