# Is the following function linear or nonlinear, from the given values of x and f(x). If it is linear, determine the slope.x y=f(x) 0 -3 2 -7 4 -11 -1 ...

Is the following function linear or nonlinear, from the given values of x and f(x). If it is linear, determine the slope.

**x y=f(x)**

0 -3

2 -7

4 -11

-1 -1

3 -9

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### 1 Answer

Let us first determine if the function f(x) in linear. If it is linear we can write f(x) = ax + b where and b have to be determined.

As f(x) = -3 for x = 0

=> b = -3

For x = 2, f(x) = -7 = 2a - 3

=> 2a = -4

=> a = -2

The function f(x) from the first two values in the table is f(x) = -2x - 3

For x = 4, f(x) = -8 - 3 = -11

For x = -1, f(x) = 2 - 3 = -1

For x = 3, f(x) = -6 - 3 = -9

It is seen that all the given values in the table of f(x) for different values of x can be arrived at by taking f(x) = -2x - 3

**The given function y = -2x - 3. The slope of the function is -2**