Question 977443
Let required line be of form y = mx+c (slope-intercept form)
Since it is perpendicular to y = 1/5 x + 6
So, product of slopes = -1 (for two perpendicular lines m1 * m2 = -1)
So m * (1/5) = -1
=> m=-5
So our line becomes,
y = -5x + c
Now, this line passes through (2,-3)  (As per ques.)
So putting the coordinates in above equation,
-3 = -5*2 +c
=> c = 7
So our line becomes,
y = -5x + 7.

Alternate method (Point slope form)
Using standard point-slope form and the condition that our line passes through (2,-3),we can write,
{{{(y-(-3))/(x-2) = m}}}
Now , we have already found m as in previous solution as m=-5
So, our line is:
{{{(y-(-3))/(x-2) = -5}}}  
=> {{{(y+3)/(x-2) = -5}}}   (Ans. in point slope form)