Question

Consider the line 3x+4y=71. What is the slope of a line perpendicular to this line?2. What is the slope parallel to this line?

Answer 1

Given:

3x+4y=7

Lets find the slope intercept form first,

$\begin{gathered} 4y=-3x+7 \\ y=-\frac{3x}{4}+\frac{7}{4} \end{gathered}$

Slope of the equation is,

$m_1=-\frac{3}{4}$

1. The slope of a line perpendicular to this line is,

Since,

$\begin{gathered} m_1m_2=-1 \\ (-\frac{3}{4})m_2=-1 \\ m_2=-1\times(-\frac{4}{3}) \\ m_2=\frac{4}{3} \end{gathered}$

Hence, the answer is

$m_2=\frac{4}{3}$

2. The slope parallel to this line is,

Since,

$\begin{gathered} m_1=m_2 \\ m_2=-\frac{3}{4} \end{gathered}$

Hence, the answer is,

$m_2=-\frac{3}{4}$