Chapter 4.1, Problem 1MRE

To determine

The equation for the linear function in the form of $f\left(x\right)=mx+b$ , if $f\left(4\right)=-6$ and $m=-2$

Answer to Problem 1MRE

The equation for the linear function is $f\left(x\right)=-2x+2$ .

Explanation of Solution

Given information: It is given that $f\left(4\right)=-6$ and $m=-2$ . And the given linear function is,

  $f\left(x\right)=mx+b\mathrm{....}\left(1\right)$

Calculation: Plugging for $\left(x=4\right)$ in (1),

  $\begin{array}{c}f\left(4\right)=m\left(4\right)+b\\ -6=\left(-2\right)\left(4\right)+b\mathrm{....}\left(\begin{array}{l}\text{By }f\left(4\right)=-6\\ \text{and }m=-2\end{array}\right)\\ \text{or, }b=2\end{array}$

Again substitute $\left(b=2\right)$ and $\left(m=-2\right)$ in (1),

  $\begin{array}{c}f\left(x\right)=\left(-2\right)x+\left(2\right)\\ f\left(x\right)=-2x+2\end{array}$

Hence, the linear function is $f\left(x\right)=-2x+2$ .