Chapter 4, Problem 11CR

To determine

To calculate: To write the linear function

Answer to Problem 11CR

Linear function is $f\left(x\right)=-4$

Explanation of Solution

Given: Values of linear function are $f\left(3\right)=-4;f\left(5\right)=-4$

Formula Used:

Equation of line passing through two points is given as

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Calculation:

Given the values of function as follows:

  $f\left(3\right)=-4;f\left(5\right)=-4$

Function passes through the points $\left(3,-4\right)$ and $\left(5,-4\right)$

Thus, equation of line is calculated as follows:

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$

Substituting the values:

  $\begin{array}{l}y-\left(-4\right)=\frac{-4-\left(-4\right)}{5-3}\left(x-3\right)\\ y+4=\frac{-4+4}{5-3}\left(x-3\right)\\ y+4=0\left(x-3\right)\\ y+4=0\\ y=-4\end{array}$

Conclusion:

Hence, linear function is $f\left(x\right)=-4$