find the constants

Question

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.

Answer 1

If f(x) = mx + b, then the slope is m.  So, m = -1.

 

Therefore, f(x) = -1x + b

 

Since f(1) = 2, we have:  f(1) = -1(1) + b = 2

                                                  -1 + b = 2

                                                         b = 3

 

f(x) = -x + 3