In the GeoGebra construction below, you're provided an x(t) curve that models such particle linear motion, with the horizontal axis representing time t and the vertical axis representing position x. Drag the "flip/shrink/flat" slider to transform the curve so that it lies flattened along the x-axis.
Now you also see a blue curve that represents the same particle motion, but in this case the horizontal axis represents position x. I recommend stopping the slider just shy of the end so that the curve is not completely flat, and you can better see the left/right motion of the blue particle/point.
To get the particle moving, either: (1) Press the "start" button, (2) Drag the "t" slider, or (3) Drag the grey point along the x(t) curve. Study how the motion of the grey point on the x(t) curve correlates to the motion of the blue point along the horizontal x-axis.