Chapter 16.1, Problem 5PS

To determine

To find: Thedistance from the point to the graph of the given equation.

Answer to Problem 5PS

The distance from the point to the graph of the given equation is $5.81\text{units}$ .

Explanation of Solution

Given information:

The given line has the slope of $2$ and passing through the point $\left(2,1\right)$ .

The equation of the line is obtained as,

  $\begin{array}{l}\left(y-y_o\right)=m\left(x-x_o\right)\\ \left(y-1\right)=2\left(x-2\right)\\ y-1=2x-4\\ 2x-y-3=0\end{array}$

The distance from the point to the graph of the given equation is calculated as,

  $\begin{array}{c}d=\frac{\left|a{x}_1+b{y}_1+c\right|}{\sqrt{a^2+b^2}}\\ =\frac{\left|2\left(-2\right)+\left(-1\right)\left(6\right)+\left(-3\right)\right|}{\sqrt{{\left(2\right)}^2+{\left(-1\right)}^2}}\\ =\frac{13}{\sqrt{5}}\\ =5.81\text{units}\end{array}$

Thus, the distance from the point to the graph of the given equation is $5.81\text{units}$ .