Find the constants m and b in the linear function f(x) = mx + b so that f(1) = 2 and the straight line represented by f has slope - 1.
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When f is written as f(x) = mx + b, then m is the slope of the function and b is the y-intercept. We are given that the slope is -1, so m = -1. Replacing that we have that:
f(x) = -x + b
Now, in order to find b we need to use the information that f(1) = 2. We do that by letting x= 1:
f(1) = 2 = -1 + b
b = 3
Therefore, the equation of the line is:
f(x) = -x + 3, so m=-1, b =3
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