Give the equation of a line that is perpendicular to y=4/5x+3 and goes through (-3,8)

Question

I would really appreciate if you could help me out with this problem :)

Answer 1

Hi Andrew,

 

The product of two perpendicular lines is  -1

 

m*m' =-1

 

You are given the first  line  y = 4/5 x +3

 

m =4/5,    4/5 *m2 = -1    this gives  m' = -5/4

 

The equation of the second line is 

y =m' x + c

 

y= -5/4 x + c but this line passes through (-3, 8)

 

8 = -5/4 *-3 + c

8 = 15/4 + c

c = 8 - 15/4 = 17/4

 

y = -5/4 x + 17/4