Liberal Arts Math Question #4

The line represented by y = 2x + 1 and a line perpendicular to it intersect at R(2, 5).

What is the equation of the perpendicular line?

$\begin{array}{|rcll|} \hline y &=& 2x + 1 \quad m = 2 \quad & \quad m_{\perp} = -\frac{1}{m} = - \frac12 \\\\ y_{\perp} &=& -\frac12\cdot x + b \quad & \quad R=(2,5) \\ 5 &=& -\frac12\cdot 2 + b \\ 5 &=& -1 + b \\ 6 &=& b \\ y_{\perp} &=& -\frac12\cdot x + 6 \\ \hline \end{array}$

The equation of the perpendicular line is $y = -\frac12\cdot x + 6$