Please help me with the question below.17. In the xy-plane, line l passes through the origin and is perpendicular to the line 4x + y = k, where...

if line l is perpendicular to 4x+y=k and goes through the
origin, then the equation of line l is:

slope of line l =
negative reciprocal of the slope of 4x+y=k

slope of
(4x+y=k) = -4

slope of line l =
1/4

equation of line l is y = x/4 or
4y=x

4(4y)+y=k                                    
substitute 4y for
x

16y+y=k

17y=k

y=k/17
--->  t+1=k/17                   substitute t+1 for y and t for
x

x=4k/17---> t=4k/17
<-------,

4k/17 +1 = k/17                   
|         substitute 4k/17 for t

4k + 17 =
k                           |         and solve for k

3k =
-17                               |

k=-17/3
----------------------'         substitute back

t =
4(-17/3)/17                               the 17 divides and cancels
out

t = -4/3

the answer is
A