ANSWER:
Paralell: -4
Perpendicular: 1/4
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]-4x-y=3[/tex]
Now, we have that an equation of a line in its slope-intercept form has the following form:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is y-intercept} \end{gathered}[/tex]
We apply it in this case:
[tex]\begin{gathered} -y=4x+3 \\ y=-4x-3 \\ \text{therefore} \\ m=-4 \end{gathered}[/tex]
When two lines are parallel, the slope is the same, while when they are perpendicular, the product of the slopes is equal to -1, we calculate each case below as follows:
[tex]\begin{gathered} \text{ Parallel} \\ m_1=m_2 \\ m_2=-4 \\ \\ \text{ Perpendicular} \\ m_1\cdot m_2=-1 \\ m_2=\frac{-1}{m_1} \\ m_2=\frac{-1}{-4} \\ m_2=\frac{1}{4} \end{gathered}[/tex]
