Question

Find the equation of the line that is perpendicular to y=-3 x+1 and contains the point (9,12)

Answer 1

Given:

`\begin{gathered} \text{ Equation of the line that is perpendicular to }y=-(3)/(4)x+1\text{ and contains} \\ \text{the point }(9,12). \end{gathered}`

Required:

Find the equation of the line.

Step-by-step explanation:

Condition for lines to be perpendicular:

`\begin{gathered} y=mx+c \\ y=-(1)/(m)x+c \end{gathered}`
`\begin{gathered} \text{ So, line is perpendicular to }y=-(3)/(4)x+1 \\ \text{ That is }y=(4)/(3)x+c \\ \text{ and contains the points }(9,12) \\ 12=(4)/(3)*9+c \\ c=0 \\ \text{ The line is }y=(4)/(3)x+0 \end{gathered}`

Answer:

`\text{ The line is }y=(4)/(3)x+0`