A linear function in the x,y plane can be written as y = mx + b. [br]For example, the linear function y = 2x +3, has the values m = 2 and b = 3. [br][i][b]We can plot this point (2,3) in the m,b plane. [/b][/i][br][br]Every linear function in the x,y plane corresponds to a point in the m,b plane. [br][br][u][b]Exploration: [/b][/u] check the EXPLORE box and experiment to see how this works.[br][br]What points in the m,b plane correspond to the functions [br]y = b, b = -1, 0, 1, 2, 3, ... in the x,y plane?[br][br]What points in the m,b plane correspond to the functions [br]y = mx, m = -1, 0, 1, 2, 3, ... in the x,y plane?[br][br][b][u]Challenge: [/u][/b] check the CHALLENGE box - a dotted line will appear in the m,b plane. [br]You can position this dotted line by dragging the two small black rings. [br]After you have placed the dotted line where you want it, [br]you can slide a large RED dot along the dotted line. [br]Each [i][b]position of the large RED dot[/b][/i] has a set of coordinates [i][b](m,b) [/b][/i][br]and therefore corresponds to a [i][b]linear function in the x,y plane[/b][/i].[br][br]As you slide the RED dot along the dotted line you will notice that [br]all the linear functions in the x,y plane pass through a single point. [br][br][u][b]YOUR CHALLENGE:[/b][/u] How is the position of the fixed point in the x,y plane [br]related to the way you placed the dotted line in the m,b plane?