Question

Find the equation of a line perpendicular to 4x - 5y = -1 that contains the point (5, -4)

Answer 1

To determine equation of a perpendicular line:

`4x-5y=-1`

Solving the above equation to determine the slope

`\begin{gathered} 4x-5y=-1 \\ \text{comapre to slope intercpet formular} \\ y=\text{ mx+c} \\ -5y=-4x-1 \\ \text{divide through by -5} \\ -(5y)/(-5)=-(4x)/(-5)-(1)/(-5) \\ y=(4)/(5)x+(1)/(5) \\ m_1=(4)/(5) \end{gathered}`

Equation of a perpendiclar line is

`\begin{gathered} m_1m_2=-1 \\ (4)/(5)m_2=-1 \\ m_2=-(1)/((4)/(5)) \\ m_2=-(5)/(4) \end{gathered}`

Then you fill in the points and change the slope to -5/4