Chapter 4, Problem 12CR

To determine

To calculate: To write the linear function

Answer to Problem 12CR

Linear function is $f\left(x\right)=-\frac{5}{3}x+18$

Explanation of Solution

Given: Values of linear function are $f\left(6\right)=8;f\left(9\right)=3$

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:

  $f\left(6\right)=8;f\left(9\right)=3$

Function passes through the points $\left(6,8\right)$ and $\left(9,3\right)$

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:

  $\begin{array}{l}y-3=\frac{8-3}{6-9}\left(x-9\right)\\ y-3=\frac{5}{-3}\left(x-9\right)\\ 3y-9=-5x+45\\ 3y=-5x+54\\ y=-\frac{5}{3}x+18\end{array}$

Conclusion:

Hence, linear function is $f\left(x\right)=-\frac{5}{3}x+18$