Question 1049998
{{{x = 4}}} is a {{{vertical}}} line.

recall: {{{y=mx+b}}} where {{{m = slope}}} and

{{{m = (change_ in_ y) / (change_ in_ x)}}}

if the slope is {{{undefined}}} because there is {{{no}}} change in '{{{x}}}', which is equivalent to dividing by {{{0}}}

A line {{{perpendicular}}} to a {{{vertical}}} line is a {{{horizontal}}} line.

 There is {{{no}}} change in '{{{y}}}', so its slope is {{{0}}}.

so, {{{y=mx+b}}} ...plug in the coordinates of given point ({{{5}}},{{{4}}}) and slope {{{m=0}}}

{{{y=mx+b}}}

{{{4=0*5+b}}}

{{{4=b}}}

so, for a horizontal line to go through the point ({{{5}}},{{{4}}}), we simply set {{{y = b}}} or:

{{{highlight(y=4)}}}

 
{{{drawing( 600, 600, -10, 10, -10, 10,
line(4,-10,4,10),circle(5,4,.12),locate(5,4,p(5,4)),
 graph( 600, 600, -10, 10, -10, 10, 4)) }}}