1

The lecturer is saying

we can then say that the gradient of this line is equal to the amount of that function that increases in this interval divided by the length of the interval

where the expression

the amount of that function that increases in this interval

is a little bit complex.

Is it grammatical and idiomatic and reasonable to simplify the expression as this

the increased amount of that function in this interval

1

It is probably just a slip of the tongue and he intended to say

we can then say that the gradient of this line is equal to the amount that the function increases in this interval divided by the length of the interval

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