Question 700324
{{{ 3y=24}}}

{{{ y=24/3}}}

{{{ y=8}}}........line parallel to {{{x-axis}}}, has {{{y-intercept of {{{8}}} and slope {{{m=0}}}


the equation of a line perpendicular to {{{ y=8}}} and passing through ({{{-7}}}, {{{11}}}) has to have a slope negative reciprocal of {{{m=0}}} which is {{{m[1]=-1/0}}} and anything divided by {{{0}}} is undefined; so, the line is vertical

now we need to find the equation of a vertical line passing through ({{{-7}}}, {{{11}}})

So the perpendicular slope is undefined ({{{m[1]=-1/0}}})

since the unknown line goes through ({{{-7}}}, {{{11}}}), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

{{{y-y[1]=m[1](x-x[1])}}}

{{{y-y[1]/m[1]=x-x[1]}}}

{{{(y-11)/1/0=x-(-7)}}}

{{{(y-11)0=x+7}}}

{{{0=x+7}}}

{{{-7=x}}}.........vertical line


{{{drawing(600,600,   -10, 10, -10, 15,  blue(line(-7,15,-7,-10)), grid(0),locate(-7,11,P(-7,11)),circle(-7,11,0.1),
graph( 600,600,   -10, 10, -10, 15,8)) }}}