Answer:
\[y = (-1/2) * x + 6\]
Explanation:
Equation of the given line: y=2x+2
Hence the slope of the line is given by 2
Any line which is perpendicular to the given line will have a slope m such that m*2 = -1
Or, \[m = \frac{-1}{2}\]
Only options 2 and 3 satisfy this condition.
The line is also supposed to pass through the point (6,3).
Substituting these values in the option 2:
\[3 = (-1/2) * 6 + 3\]
Or, \[ 3 =0 \] which is false . Hence option 2 is not valid.
Now substituting (6,3) in option 3:
\[3 = (-1/2) * 6 + 6\]
Or, \[ 3 =3 \] which is true . Hence option 3 is the required equation of the line.