Find the equation of a line perpendicular to 2x+8y=17 and passing through the point (1,2).

Question

College Algebra

Answer 1

2x + 8y = 17

 

        8y = -2x + 17

 

         y = (-1/4)x + 17/8

 

So the slope of the line with equation 2x + 8y = 17 is -1/4.

 

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

 

Equation of line with slope 4 and containing the point (1,2) is y - 2 = 4(x - 1)

 

                                                                                        y - 2 = 4x - 4

 

                                                                                             y = 4x - 2

 

Answer 2

The slope of a line Ax+By=C (Standard Form) is (-A/B).   [note: convert this once and for all to y=mx+b and remember it].

 

The slope of all perpendicular lines is the negative reciprocal of the slope of this line (that is, B/A).  So, all perpendicular lines have the formula:

       8x-2y=C       [and we need point (1,2) to determine C]

 

       8(1)-2(2)=C

         8-4 = C

           4 = C

 

The equation of the perpendicular line, in Standard Format, is:    4x - y = 2    [reduced from 8x-2y=4]