Find the equation of the line containing the point P(4,5) and perpendicular to the graph of y=5/4x-1? Help please!!!!

Question

 Algebra question 

Answer 1

The line y = (5/4)x - 1 has slope 5/4

 

Any line perpendicular to the given line has slope -1/(5/4) = -4/5

 

Equation of line with slope -4/5 and containing the point (4,5):

 

     y - 5 = (-4/5)(x - 4)

 

          y = (-4/5)x + 41/5    or 4x + 5y = 41

 

Answer 2

Its slope must be the negative reciprocal of the slope of the given line.

 

m = -1/(5/4) = -4/5

 

In point-slope form,

 

y - y₁ = m(x - x₁)

 

y₁ = 5

x₁ = 4

m = -4/5

 

y - 5 = (-4/5)(x - 4)

 

You may express this in standard form or some other form if you wish.