If two lines are perpendicular, the slope of one of the lines is the negative reciprocal of the other. Since we know the slope for one of our lines, [tex]2[/tex]m lets find the other:
[tex]m=- \frac{1}{2} [/tex]
Now, lets use the point-slope formula to complete the equation of our perpendicular line:
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y-5=- \frac{1}{2} (x-2)[/tex]
[tex]y-5=- \frac{1}{2}x+1 [/tex]
[tex]y=- \frac{1}{2} x+6[/tex]
We can conclude that our perpendicular line is [tex]y=- \frac{1}{2} x+6[/tex]
