Show that f is linear of slope m if and only if f(x + h) - f(x) = mh (for all x and h)That is to say, prove the following two statements:(a) f is linear of slope m implies that f(x + h) - f(x) = mh (for all x and h ).(b) f (x + h) - f (x) = mh (for all x and h) implies that f is linear of slope m.
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Show that f is linear of slope m if and only if f(x + h) - f(x) = mh (for all x and h)
That is to say, prove the following two statements:
(a) f is linear of slope m implies that f(x + h) - f(x) = mh (for all x and h ).
(b) f (x + h) - f (x) = mh (for all x and h) implies that f is linear of slope m.
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