 Hello friends so this is a GeoGibra tool so we are going to visualize how does a linear equation in two variables is represented and in a coordinate plane you know xy plane so we have if you see we have taken an equation over here x plus y plus 1 equals to 0 so this equation is basically you know a special case of ax plus by plus c where if you can see a is equal to 1 b is equal to 1 and c is equal to 1 this is how the equation look when visualized in a graphing tool. Now if I just want to explore what happens if I keep changing the values of a b and c and how does the the equation or the graph of the equation behave. So here I have a equals to 1 in this equation so let us say if I change the value of a in the linear equation so if I increase I am now increasing this value of a can you see the line is now rotating rotating around a fixed point let me just find that point out first so if you take point let me just you know this is the point of intersection of so the line and the y axis so the point of intersection is there is 0 and minus 1 so if I change the value of a nothing changes as in the point of intersection of the line and the y axis doesn't change and if you see as I am reducing the value of a the line is going in anticlockwise direction as I am increasing the a the line goes in a clockwise direction that's how it's behaving so hence it is covering the entire xy plane is it now I'm going to fix this value a to 1 okay now what happens if I change b so if you change b again so if I am increasing can you see it is going in anticlockwise direction and again here if you see the point of intersection of the line and the y axis is changing but the point of intersection of point of intersection of the line and the x axis is not changing so I am again going to fix this point let us say this is the point b okay minus 1 comma 0 so now let me change the value of b again so if you see the point of intersection of x axis and the line is not changing but the point of intersection of y axis and the line is changing isn't it so this is how the visualization or the graph changes as you keep on varying the value of a and b what happens if I change the value of c let us see the effect of changing the value of c so if I change the value of c if you can see I am changing the value of c but unfortunately it's not changing why because we have kept we have to just delete these points because we had to fix these points so hence now let me just delete this point so that there is no constraint on in on the line now if you change the c value can you see it's changing it's shifting it's translating we say that the line is shifting or translating and if I increase the value of c it is going leftwards right and if I decrease the value of c it is going rightwards or in the other other way of looking at it is if you decrease the value of c it is going upwards and if you increase the value of c it is going downwards isn't it and there's one case which I wanted to highlight is then is that when c becomes 0 so if you see c is 0 now in such case the line passes through the origin so now you change keep on changing the value of a and b the line will always pass through origin right will always pass through origin so what is the condition for the line to be passing through origin the c value must be 0 right so you can now you know use this software and try tweaking a b and c and try and see how the graphs changes or how how the visualization of the linear equation changes when you change a b and c thank you