In analytic geometry, using the common convention that the horizontal axis represents a variable x {\displaystyle x} and the vertical axis represents a variable y {\displaystyle y} , a y {\displaystyle y} -intercept or vertical intercept is a point where the graph of a function or relation intersects the y {\displaystyle y} -axis of the coordinate system. As such, these points satisfy x = 0 {\displaystyle x=0} .