Chapter 3.9, Problem 4WE

To determine

To find: An equation of the linear function $f$ .

Answer to Problem 4WE

Therefore, the equation of linear function $f\left(x\right)=\left(-\frac{3}{2}\right)x-\frac{1}{2}$ .

Explanation of Solution

Given information: The slope and function $f\text{ at }x=0$ ,

  $m=-\frac{3}{2},f\left(0\right)=-\frac{1}{2}$

Formula used: For calculation of equation of linear function,

  $\begin{array}{l}f\left(x\right)=mx+b\\ \text{where }m\text{ is slope and b is }y-\text{intercept}\text{.}\end{array}$

Calculation: To calculate the equation of function using slope and function $f\text{ at }x=0$ ,

  $\begin{array}{l}\text{Putting value of }m\text{in genral form,}\\ f\left(x\right)=\left(-\frac{3}{2}\right)x+b\\ \text{Now, at }x=0\\ f\left(0\right)=\left(-\frac{3}{2}\right)\times 0+b\\ b=-\frac{1}{2}\\ f\left(x\right)=\left(-\frac{3}{2}\right)x-\frac{1}{2}\end{array}$

Therefore, the equation of linearfunction $f\left(x\right)=\left(-\frac{3}{2}\right)x-\frac{1}{2}$ .