Chapter 0, Problem 13RE

To determine

To calculate : The equation of specified line for the given points.

Answer to Problem 13RE

The equation of specified line is $y=-\frac{1}{2}x+3$ .

Explanation of Solution

Given information :

The given $x$ and $f\left(x\right)$ values are:

  $\begin{array}{l}x=-2,f\left(x\right)=4\\ x=2,f\left(x\right)=2\\ x=4,f\left(x\right)=1\end{array}$

Calculation:

Write the coordinates for the given values are $\left(-2,4\right),\left(2,2\right)\&\left(4,1\right)$ .

Find the slope of the line that passes through the points $\left(2,2\right)\&\left(4,1\right)$ .

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{1-2}{4-2}\\ m=\frac{-1}{2}\\ m=-\frac{1}{2}\end{array}$

Write the equation of line whose slope is $-\frac{1}{2}$ and passes through the point $\left(2,2\right)$ .

The point slope form of the line is $y-y_1=m\left(x-x_1\right)$ .

  $\begin{array}{l}y-2=-\frac{1}{2}\left(x-2\right)\\ y-2=-\frac{1}{2}x+1\\ y=-\frac{1}{2}x+1+2\\ y=-\frac{1}{2}x+3\end{array}$

Therefore, the equation of specified line is $y=-\frac{1}{2}x+3$