# 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

justaguide | College Teacher | (Level 2) Distinguished Educator

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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