Chapter 4.3, Problem 8Q

To determine

To calculate: To write the linear function

Answer to Problem 8Q

Thelinear function is $y=-6$

Explanation of Solution

Given: $f\left(-1\right)=-6;f\left(4\right)=-6$

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:

  $f\left(-1\right)=-6;f\left(4\right)=-6$

This means that at $x=-1$ , $y=-6$ and $x=4$ , $y=-6$

Equation of function is found by finding the equation of line passing through $\left(-1,-6\right)$ and $\left(4,-6\right)$

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:

  $\begin{array}{l}y-\left(-6\right)=\frac{-6-\left(-6\right)}{4-\left(-1\right)}\left(x-\left(-1\right)\right)\\ y+6=\frac{-6+6}{4+1}\left(x+1\right)\\ y+6=0\left(x+1\right)\\ y+6=0\\ y=-6\end{array}$

Conclusion:

Hence, the linear function is $y=-6$