A movable tangent line
For \(f(x)=x^2\), the tangent’s slope depends on where we draw it. Move the red point and pay attention to how the line’s tilt changes.
Drag the red point or change \(a\) in the expressions panel. Notice what happens at \(a=0\).
What you’re seeing
At the chosen point \(x=a\), the tangent line has slope \(2a\). Its equation is \(y=2ax-a^2\). Moving the point changes both the location and tilt of the line.