now in this lesson we look at graphing straight lines using the intercepts now we need only to find two points that satisfy the equation and then draw a straight line passing through these points and the best points to find are where the line cuts the x-axis and the y- AIS to do this we let xal not and that will give us the Y inter okay in other words where it cuts the Y AIS and then we also let y equal n and that will give us the x intercept in other words where it cuts the x axis so that's some important information there let xal N gives us the Y intercept let yal 0 that gives us the x intercept let's look at some examples we are asked to draw the line 2x + y = 4 now now there's our little graph there we'll work from that first step let x equal 0 so when x equal 0 we substitute for X we substitute zero there and we get 2 * 0 + y = 4 and 2 * 0 of course is nothing so really we simply have y = 4 so we have X is not Y is four that's the point not four so we can plot that point on our graph all right you can see that's the Y intercept our next step is to find the x intercept by letting y = 0 so when Y is z we substitute into our equation we get 2x + 0 = 4 and 2x + 0 is simply 2x so we simply have 2x = 4 and if 2x = 4 of course then therefore X must equal to 2 so what have we got we've got x = 2 and and Y = 0 so the point there is 20 and on the graph that's where it is okay you can see that's where it cuts the x axis so we've got our two points now we need to draw a straight line passing through these points there it is and recall our earlier work on graphing we always make sure we label the graph excellent now recall then xal 0 gives us the y intercept y = 0 gives us the x intercept let's look at doing some further examples the second one we need to draw the line y = 3x - 6 again we draw a graph now the firstly the Y intercept let X = 0 we substitute that into the equation we get that y = 3 * 0 - 6 and 3 * 0 is nothing take away 6 is -6 so we get that therefore y = -6 so the point x is 0 Y is -6 that is this point and we plot that on the graph so it's down there that is our Y intercept now let's try for our x intercept by letting yal 0 so when Y is z we substitute that into the equation we get 0 = 3x - 6 so we need to solve that equation equation we take the -6 over becomes POS 6 so 6 = to 3x and therefore X = to two so our point x is 2 Y is 0 has coordinates 2 0 and we plot that particular Point again on the graph all right that will be our x intercept so we have our two points we draw the line through the points and we label the graph okay not too hard is it we'll do one more example here's our third example draw the line y = 2x so again start by drawing up a number plane x = 0 gives us our Y intercept so when x is 0 we substitute that in we get Y = 2 * 0 and that's not too hard to work out we get yal 0 so we have X is z y is z coordinates 0 0 so there's our point there right can you recall what that point is called It's called The Origin now our x intercept well we let yal 0 we substitute that into the equation we put yal 0 we get 0 = 2X and solving that we get therefore that X is0 as well so X is0 Y is0 okay but that point we've already got it there haven't we it's the same point Point as the one before so when that's the case we need to find another Point all right it's very hard to draw a straight line if we've only got one point we're dealing with so we need to find another point so we can do that by say let X = 3 we could just choose any value of x really but when xal 3 is a good one that'll fit on the graph we substitute that into the equation we get Y = 2 * 3 and Y = 2 * 3 of course therefore y 6 so we have the point where X is 3 Y is 6 so the coordinates are 3 6 and we plot that onto the graph okay last step then draw the line through and can you recall what the very last step is of course to write the equation of the line excellent well that concludes our lesson good luck with your questions