Coordinate Graphs, Lines & Slope

origin

The origin is the “you are here” point of the coordinate plane — the spot where measuring begins. Every set of directions, like “3 right and 2 up,” starts from here.

It is the single point where the x-axis and y-axis cross, with coordinates (0, 0). Both coordinates are zero because you have not moved horizontally or vertically away from the starting point.

The origin is a useful landmark: a line through the origin has equation y = mx (no constant term), and direct variation is exactly the family of lines that pass through it.

The line y = 2x passes through the origin: when x = 0, y = 2·0 = 0, giving the point (0, 0).

Lines with no constant term pass through (0, 0).