Chapter 8.4, Problem 40WE

To determine

To Find: The value of $d$ .

Answer to Problem 40WE

Value of d is 9 when $dy+3x=2$ is parallel $x-3y=0$ and Value of d is 0 when $dy+3x=2$ is parallel y-axis.

Explanation of Solution

Given information:

  $dy+3x=2$ is parallel $x-3y=0$ .

Formula used: -

Slope form of line: $y=mx+c$ .

Where $m$ is the slope of line, and $c$ is the $y$ -intercept when $x=0$ .

Slope of parallel lines with slope $m_1$ and $m_2$ is $m_1=m_2$

As we know, $dy+3x=2$ is parallel $x-3y=0$ .

So, solving for slope of $dy+3x=2$

  $\begin{array}{l}dy+3x=2\\ dy=-3x+2\\ y=\frac{-3}{d}x+\frac{2}{d}\end{array}$

  $m_1=\frac{-3}{d}$

So, solving for slope of $x-3y=0$

  $\begin{array}{l}-3y=x\\ y=\frac{x}{-3}\\ y=-\frac{1}{3}x+0\end{array}$

  $m_2=-\frac{1}{3}$

Recall that Slope of parallel lines with slope $m_1$ and $m_2$ is $m_1=m_2$ .

  $\begin{array}{l}\frac{-3}{d}=-\frac{1}{3}\\ 3\cdot 3=d\\ 9=d\end{array}$

Value of d is 9 when $dy+3x=2$ is parallel $x-3y=0$ .

When $2y+px=5$ is parallel y-axis.

The coefficient of y in equation of a line parallel to y-axis is 0.

As d is coefficient of y in this situation,

  $d=0$

Value of d is 0 when $dy+3x=2$ is parallel y-axis.