please solve the following algebra problem

Question

Write the slope-intercept form of the equation of the line passing through (4, -1) and perpendicular to 3x + 12y = 5

Answer 1

Perpendicular lines have slopes that are negative reciprocals of each other. 

find the slope of the given line  3x+12y =5

Put it in y-intercept form so that the slope is easy to see

3x/12 +12y/12 =5/12

y=-3x/12 +5/12  simplify

y=-1x/4 +5/12

Slope is -¼ and the slope of all lines ⊥ is 4/1

Since we know the slope and a point (4,-1) we can write an equation in two-point form

y-(-1) =4(x-4) 

y+1=4(x-4)

y+1=4x-16

In y intercept form

y=4x -17

 

 

Answer 2

3x + 12y = 5

 

Solve for y to put the equation in slope-intercept form:

 

     12y = -3x + 5

         y = (-1/4)x +(5/12)    Slope = -1/4

 

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

 

Equation of line with slope 4 and passing through (4, -1):

 

       y - (-1) = 4(x - 4)

 

      y + 1 = 4x - 16

 

             y = 4x - 17