i have a given point of (3,2)
i know that the slope is 2 and if i move two up i will have y equals 4
but why should i move 1 to the right?
the slope is 2 so i will move to up but why 1 to the right which leads to (4,4)?
The slope is the ratio of the vertical change to the horizontal change. When the slope of a line is 2 and (x, y) is on the line, then for any number z the point (x + z, y + 2z) is again on the line. Here the vertical change from (x, y) to (x + z, y + 2z) is 2z and the horizontal change is z.
If a line is sloped, then to move along the line and stay on it you need to move along both the y- and x-axes. The slope of the line is by definition the ratio of those displacements. If you move strictly up, then you leave the line.
ok one final remark on the matter then.
if you say that going 1 to the right means going 2 up by definition i would expect that going 10 to the right would not change the definition of the slope and expect to go only 2 up in such case or is the rule based differently?