Chapter 4.2, Problem 24E

To determine

To calculate: To write the linear function

Answer to Problem 24E

The linear function is $f\left(x\right)=4$

Explanation of Solution

Given: $f\left(-10\right)=4;f\left(-2\right)=4$

Formula Used:

Equation of line in slope intercept form is given as:

  $y=mx+c$ , where $\begin{array}{l}m=slope\\ c=y-intercept\end{array}$

Also, 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 that values of linear function as follows:

  $f\left(-10\right)=4;f\left(-2\right)=4$

This means that at $x=-10$ , $y=4$ and $x=-2$ , $y=4$

Equation of function is found by finding the equation of line passing through $\left(-10,4\right)$ and $\left(-2,4\right)$

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 in above equation:

  $\begin{array}{l}y-4=\frac{4-4}{-10-\left(-2\right)}\left(x-\left(-2\right)\right)\\ y-4=\frac{0}{-10+2}\left(x+2\right)\\ y-4=0\left(x+2\right)\\ y-4=0\\ y=4\end{array}$

Conclusion:

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