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What is the rate of change of the function?

-5-
0/- &
4
23
Mark this and return
2.3
5
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What is the rate of change of the function? -5- 0/- & 4 23 Mark this and return-example-1
User GusOst
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1 Answer

14 votes
14 votes

Explanation:

the change rate or slope is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

formally, in an interval [a, b] the change rate is therefore

(f(b) - f(a))/(b - a)

in the graph we look for points with integer coordinates.

like (3, 5) or (2, 2) or (0, -4).

so, let's use any pair of them, e.g. (3, 5) and (2, 2).

the direction from what point to what point does not matter, as long as we use the same for x and y.

say, we go from (2, 2) to (3, 5) :

x changes by +1 (from 2 to 3).

y changes by +3 (from 2 to 5).

so, the slope or change rate is

+3 / +1 = 3

FYI - if we go from (3, 5) to (2, 2)

x changes by -1 (from 3 to 2).

y changes by -3 (from 5 to 2).

so, the slope is

-3 / -1 = 3

so, you see the direction does not matter. the slope is the same.

User Mitya Ustinov
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2.8k points