Fuctions

[Guest]

Function f is defined by f : x --> mx + c.
Given f(2) = 7 and f(4) = -1
find the value of m and of c

the answer is m = -4, c = 15
I just cant seem to find the answer

[Guest]

We know that
f(2) = 7
f(2) = 2m + c = 7

and
f(4) = -1
f(4) = 4m + c = -1

So we need to solve these simultaneous equations.
2m + c = 7
4m + c = -1

From the first equation we find c = 7 - 2m
and replace c in the second
4m + 7 - 2m = -1
2m = -1 - 7
2m = -8
m = -4

c = 7 - 2m = 7 - (-8) = 7 + 8 = 15

[Guest]

Another way of solving 2m+ c= 7 and 4m+ c= -1:

Observing that both equations have "+ c" we see that subtracting one equation from the other will eliminate c. Subtractuinng the second equation from the first, -2m= 8 so m= 8/(-2)= -4.

Then 2m+ c= 2(-4)+ c= -8+ c= 7.

Adding 8 to both sides c= 15.