Chapter 4.2, Problem 21E

To determine

To calculate: The linear function f with the given values $f(2)=-2,f(1)=1$ .

Answer to Problem 21E

The linear function is $f(x)=-3x+4$ .

Explanation of Solution

Given information: The given values is $f(2)=-2,f(1)=1$ .

Calculation: The given values is $f(2)=-2,f(1)=1$

  $m=\frac{y_2-y_1}{x_2-x_1}\left[1\right]$ .

The equation for the slope, of a line is:

  $m=\frac{y_2-y_1}{x_2-x_1}\left[1\right]$

The equation $f(2)=-2$ tell us that $x_1=2\mathrm{and}{y}_1=-2;$ and $f(1)=1$ tell us that $x_2=1\mathrm{and}{y}_2=1;$ substitute this into equation $(1)$ .

  $m=\frac{1+2}{1-2}=\frac{3}{-1}=-3$

Substitute value of $m=-3$ $x=2\mathrm{and}y=-2;$ ,into equation $y=mx+c$

  $\begin{array}{l}-2=-3\times -2+c\\ -2=-6+c\\ -2+6=c\\ 4=c\end{array}$

Substitute m=-3 and c=4 in $y=mx+c$

  $y=-3x+4$ .

Thus, the equation of the function $f(x)=-3x+4$ .