# Find the equation of a line passing through (-4,-5) and perpendicular to the line joining points (1,2) and (5,6)

$\begin{array}{l}\text{Given that,}\\ \text{Line is passing through }\ \left(-4,\ -5\right)\ \&\ \text{perpendicular to line joing points}\ \left(1,2\right)\ \&\ \left(5,6\right)\\ \text{As we know, }\\ y-y_1=m\left(x-x_1\right)\ \&\ \text{If line are perpendicular then slopes,}\ m_1m_2=-1\\ \text{slope of given line }\left(m_1\right)=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}=\frac{\left(6-2\right)}{\left(5-1\right)}=1,\ \\ m_1m_2=-1\\ \Rightarrow m_2=-1\\ \text{Now we put in equation,}\\ y-y_1=m_2\left(x-x_1\right)\\ y-\left(-5\right)=-1\left(x-\left(-4\right)\right)\\ \Rightarrow y+x=1\\ \\ \end{array}$

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