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Question

# The linear function f is defined by f(x) = cx + d, where c & d are constants. If f (50) = 27,000 and f (100) = 38,000, what is the value of c?

## The correct answer is: 220

### Substituting the values of x = 50 & x = 100 in the given function, we will get 2 linear equations. Solving them simultaneously will give the value of c = ?

Step-by-step solution:-

f (x) = cx + d

i. For f (50) -

f (50) = c (50) + d

27,000 = 50c + d ________________. (From Given) _______________ (Equation i)

ii. For f (100)-

f (100) = c (100) + d

38,000 = 100c + d ___________________. (From Given) ________________(Equation ii)

Subtracting equation i from ii, we get-

Final Answer:-

∴ For the given linear function, the value of c = 220

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