Chapter 16.1, Problem 4PS

To determine

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

Answer to Problem 4PS

The distance from the point to the graph of the given equation is $4\text{units}$ .

Explanation of Solution

Given information:

The given equation is,

  $3x-4y=14$

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

  $\begin{array}{c}d=\frac{\left|a{x}_1+b{y}_1+c\right|}{\sqrt{a^2+b^2}}\\ =\frac{\left|3\left(6\right)+\left(-4\right)\left(-4\right)+\left(-14\right)\right|}{\sqrt{{\left(3\right)}^2+{\left(-4\right)}^2}}\\ =\frac{20}{5}\\ =4\text{units}\end{array}$

Thus, the distance from the point to the graph of the given equation is $4\text{units}$ .