It all depends on what shooting mode you have selected regarding the influence in the change of shutter speed, aperture etc.

Manual: You will have full control over all settings to get the correct exposure - changing the shutter speed will not influence the settings of the aperture, they all need to be manually set depending on your meter readings.
Aperture Priority: You control the desired aperture but the camera chooses the shutter speed depending on meter readings.
Shutter Priority: You control the desired shutter speed but the camera chooses the aperture speed depending on meter readings.
Program/Auto: The camera does all the choosing for you based on the meter readings.

I generally always shoot in manual as it offers full control over the exposure.

If you do have a zoom lens that does change the aperture size as you zoom in, the influence on shutter speed will depend on the shooting mode you are in.

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Paul