For this case we have that by definition, the equation of a line in the point-slope form is given by:
[tex]y-y_ {0} = m (x-x_ {0})[/tex]
Where:
m: It is the slope of the line and [tex](x_ {0}, y_ {0})[/tex]is a point through which the line passes.
We have the following equation of the slope-intersection form:
[tex]y = 4x + 1[/tex]
Where the slope is [tex]m = 4[/tex]
By definition, if two lines are perpendicular then the product of their slopes is -1.
Thus, a perpendicular line will have a slope:
[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {4}\\m_ {2} = - \frac {1} {4}[/tex]
Thus, the equation will be of the form:
[tex]y-y_ {0} = - \frac {1} {4} (x-x_ {0})[/tex]
Finally we substitute the given point and we have:
[tex]y-3 = - \frac {1} {4} (x-6)[/tex]
Answer:
Option B
