Chapter 1, Problem 36RE

To determine

To find:The Equation of the line

Answer to Problem 36RE

The equation of the line in general form is $x+3y=10$

Explanation of Solution

Given:

Perpendicular to the line $3x-y=-4$

  $\left(-2,4\right)$

Formula Used:

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

Calculation:

Equation of the line in point-slope form:

  $y-y_1=m\left(x-x_1\right)$

Where $m$ is the slope and $\left(x_1,y_1\right)$ is a point of the line.

An equation of the line with slope $-\frac{1}{3}$ and containing the point $\left(-2,4\right)$ can be found by using

the point-slope form with $m=-\frac{1}{3},x_1=-2$ and $y_1=4$ .

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-4=-\frac{1}{3}\left[x-\left(-2\right)\right]\\ y-4=-\frac{1}{3}x-\frac{2}{3}\\ y=-\frac{1}{3}x+\frac{10}{3}\end{array}$

Continue further with the algebra for the general form:

  $\begin{array}{l}y=-\frac{1}{3}x+\frac{10}{3}\\ 3y=-x+10\\ x+3y=10\end{array}$

Conclusion:

Therefore, the equation of the line in general form is $x+3y=10$