Question 1006535
If the points ({{{4}}},{{{2}}}) and ({{{-1}}},{{{k}}}) are on a line that is perpendicular to the line {{{y=2x+1}}}, what is the value of {{{k}}}? 

the line {{{y=2x+1}}} has a slope {{{2}}}
a line that is perpendicular to the line {{{y=2x+1}}} will have a slope {{{-1/2}}} (negative reciprocal)

so, its equation, so far, is {{{y=-(1/2)x+b}}}

since it passes through the points ({{{4}}},{{{2}}}) , we will use it to find {{{b}}}

{{{y=-(1/2)x+b}}}

{{{2=-(1/2)4+b}}}

{{{2=-2+b}}}

{{{b=4}}}

so, equation is:

{{{y=-(1/2)x+4}}}


now use ({{{-1}}},{{{k}}}) to find {{{k}}} which represents {{{y}}} coordinate


{{{k=-(1/2)(-1)+4}}}

{{{k=1/2+4}}}

{{{k=1/2+8/2}}}

{{{k=9/2}}}

so, the point is ({{{-1}}},{{{k}}}) =({{{-1}}},{{{9/2}}}) 


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(4,2,.12),circle(-1,9/2,.12),
locate(4,2,p(4,2)),locate(-1,9/2,p(-1,9/2)),
 graph( 600, 600, -10, 10, -10, 10, 2x+1, -(1/2)x+4)) }}}