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=-(3x)/(4)+(7)/(4) \end{gathered}`

Slope of the equation is,

`m_1=-(3)/(4)`

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

Since,

`\begin{gathered} m_1m_2=-1 \\ (-(3)/(4))m_2=-1 \\ m_2=-1*(-(4)/(3)) \\ m_2=(4)/(3) \end{gathered}`

Hence, the answer is

`m_2=(4)/(3)`

2. The slope parallel to this line is,

Since,

`\begin{gathered} m_1=m_2 \\ m_2=-(3)/(4) \end{gathered}`

Hence, the answer is,

`m_2=-(3)/(4)`