Q20. - Algebra 2

Question

State whether each equation or function is linear. Write yes or no. If no, explain your reasoning.

 

$f\left(x\right)=6x-19$

Step-by-Step Solution

Answer

Yes, the function $f\left(x\right)=6x-19$ is a linear function.

Step 1 – Definition of a linear equation and linear function.

In a linear equation the exponent of each variable is 1 and the variables may not be multiplied together. The graph of a linear equation is always a line.

 

In a linear function, each input value has a unique output value. In other words, for each point in domain, there is a unique value in the range of function. It can be written as $f\left(x\right)=mx+b$, where m and b are real numbers.

Step 2 – Given information.

The given function is:

$f\left(x\right)=6x-19$

Step 3 – Check whether the equation is linear or not.

The given function is in the form of $f\left(x\right)=mx+b$, where both m=6 and b=-19 are real values. So, the function $\mathit{f}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{=}\mathbf{6}\mathit{x}\mathbf{-}\mathbf{19}$ is a linear function.

 

Thus, the required answer is “Yes” because the function $f\left(x\right)=6x-19$ is a linear function.