The line shifts upwards when c is changed from c = -4 to c = 4[br]The gradient of the line remains unchanged.[br][br]The value of c is the y coordinate of the point where the line cuts the y axis (y intercept)[br][br]On the y axis, x = 0[br]y = m (0) + c [br]so y = c (the y intercept or the y coordinate of the point where line meets the y axis)

The gradient (or the direction of the line) changes from decreasing (sloping down ) to increasing (sloping up) in the positive x direction.[br]The line rotates about the point where the line cuts the y axis![br][br]In the equation y = mx + c, since c is the y intercept (from above question), when only m changes, the value of c remain unchanged, hence the line has to cut the y axis at y = c all the time as m changes.[br]Hence the line is rotating about (0, c), which acts as the centre of rotation. [br]

The new line 6x - 2y = 4 has the same gradient and y intercept as the original line y = 3x - 2.[br][br]By balancing and manipulating the equation 6x - 2y = 4, [br] 2y = 6x - 4[br] y = 3x - 2[br][br]hence the two equations are actually equivalent equations since all the pairs of x and y values of points along the two lines are identical.[br]