Why does the slope of a PT Graph equal the VT graph?

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The slope of a position-time (PT) graph represents velocity, calculated as the change in position over the change in time. This relationship is established because the slope formula, ΔY/ΔX, translates to meters per second when Y is position and X is time. Consequently, the slope directly indicates the rate of change of position, which is defined as velocity. Understanding this connection clarifies why the slope of a PT graph equals the corresponding value on a velocity-time (VT) graph. This fundamental concept illustrates the relationship between position, time, and velocity in physics.
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Can someone please explain this to me (please see title)? I understand how to compute it but why is this so?

Thanks
 
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You mean momentum-time graph and velocity-time graph?
 
or is it the pressure-temperature and volume-temperature graph for ideal gases?
 
I mean Position-Time and Velocity-Time.
 
What does slope mean?

Slope = \frac{\Delta Y}{\Delta X}

What is your Y-axis? position (meters)
What is your X-axis? time (seconds)

Therefore,

Slope = position/time = meters/seconds = velocity

Velocity is the change of rate of change of position per unit time.
 

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