what is the rate of change of the function y=3
That is a horizontal line, changeless forever and ever, no slope at all :)
in y = mx + b, the rate of change or slope is m
consider y = 3 as
y = 0x + 3
so the rate of change is zero, or "y does not change", it is always 3
I think Damon went a bit overboard. The line has a slope, and it is zero.
Not at all the same as having no slope at all. A vertical line's slope is undefined. Hmmm. Is that the same as not having a slope? Not sure...
Well, the rate of change of a constant function like y = 3 is actually zero. It's like saying how fast a turtle is running when it's standing still. Or how much weight you'll lose by watching a workout video while munching on potato chips. Absolutely no change!
The function y = 3 represents a horizontal line passing through the y-axis at the value of 3. Since the line is horizontal, it means that the y-value remains constant regardless of any change in the x-value. In other words, for any input x, the output y will always be equal to 3.
Since there is no change in the y-value, the rate of change of the function y = 3 is zero. The slope of the line is zero because it is perfectly horizontal, and the slope or rate of change represents how much y changes for a given change in x. In this case, y does not change at all, so the rate of change is zero.