Question

I have a question of how do I determine the variables when graphing linear equation? For an example graph x+2y=4, how do you come up with the variables as (0,2) (2,1) and (4,0)? The example in my book does not tell me how they came up with this. I know how to graph, I need to know how to come up with the variables.

Answer 1

basically, you pick any variable you want, and let the equation calculate the corresponding second variable.

e.g. pick y=2, (one of their answer points)
then x+2(2)=4
x+4=4
so x=0, then when x=0,y=2, which is the point (0,2)
(the x is always written first, the y second)

in general one would isolate one of the variables, in this case I would say
x=4-2y
Now by choosing any y value you want, you would generate a matching x value.
e.g. let y =8, then
x=4-2(8)
x=-12 --------> point would be (-12,8) etc