Chapter 8.4, Problem 38WE

To determine

To Find: Equation of line which satisfies given equation.

Answer to Problem 38WE

The equation of required line is $y=4x+9$ .

Explanation of Solution

Given information:

Required line has same y-intercept as of $4y+x=36$ .

Required line is parallel to $y-3x=4$ .

Formula used:

Slope-intercept line: $y=mx+c$ .

Where m is slope of line, and c is y-intercept of line.

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

As we know, Required line is parallel to $y-3x=4$ .

As we know, Slope of parallel lines with slope $m_1$ and $m_2$ , $m_1=m_2$

So, solving for slope of $y=5x-3$

  $\begin{array}{l}y-3x=4\\ y=3x+4\end{array}$

  $m=4$

Given that Required line has same y-intercept as of $4y+x=36$ .

So, solving for y-intercept of $4y+x=36$ .

  $\begin{array}{l}4y+x=36\\ 4y=-x+36\\ y=-\frac{1}{4}x+\frac{36}{4}\\ y=-\frac{1}{4}x+9\end{array}$

  $y-intercept=9$

As we know, Slope-intercept line: $y=mx+c$ .

Where m is slope of line, and c is y-intercept of line.

We have $m=4,c=9$

  $\begin{array}{l}y=mx+c\\ y=4x+9\end{array}$

The equation of required line is $y=4x+9$ .