Linear function f(x)=bx and its slope function

Click and drag on the point A to see the slope of the function traced. Click the reset button (top right hand corner) and then click and drag on the slider 'linear function' to change the function.

Note the slope function. It is always a constant. The slope of the line is constant, it has the same value everywhere on the line. Can you work out the equation of the slope function?