There's no way a throttle cable will stretch.
Steel line has no stretch, at least when examining the pulling apparatus, the throttle.
There are parts that may extrude, bend or wear to make slack in the line but the cable won't stretch.
Before a cable stretches, the ends on the cable will pull off. So look elsewhere for the reason for the slack.
And for those that take exception to this statement, please note that I am talking about the cable only, the part that is doing the work. Not the outside covering or anything else.
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Au contraire. Steel cable most assuredly stretches (but not 1/2" in that short of a run, not under the minimal load of a throttle cable and not if its been installed a while). New cable stretches. When we used to fabricate control cable, we had to pre-stretch it otherwise you'd be farting around with it for a week, trying to keep the cable tension within spec. Most cable comes pre-stretched now.
-RP