Explanation
Step 1
find the slope of the given line
Let
P1(0,3)
P2(6,2)
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]replace
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope_1=\frac{2-3}{6-0}=\frac{-1}{6}=-\frac{1}{6} \end{gathered}[/tex]Step 2
2 lines are perpendicular if
[tex]\begin{gathered} \text{slope}_1\cdot slope_2=-1 \\ \text{replace} \\ -\frac{1}{6}\cdot slope_2=-1 \\ \text{slope}_2=-1\cdot-6 \\ \text{slope}_2=6 \end{gathered}[/tex]so, the line we need to find has slope =6 and passes through the poitn (4,5)
Step 3
finally , find the equation of the line
Let
slope=6
P1(4,5)
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