Exploring the effect of changing axes on the equation of a straight line

This graph shows a point on a line of gradient m passing through the point [math](x_1,y_1)[/math].[br]You can control the gradient of the line with the slider, you can move the point [math](x_1,y_1)[/math] and you can move the red point.[br]What condition do the coordinates of the red point satisfy in the blue axes (the (X,Y) coordinates)?[br]How are the blue coordinates (X,Y) related to the black coordinates (x,y)?[br]What condition do the coordinates of the red point satisfy in the black axes (the (x,y) coordinates)?