Question 161816
First put your equation into slope-intercept form, {{{y=mx+b}}}.
{{{x-4y=48}}}
{{{-4y=-x+48}}}
{{{y=(1/4)x-12}}}
The slope of the line is (1/4) or
{{{m[1]=(1/4)}}}
Perpendicular lines have slopes that are negative reciprocals of each other,
{{{m[1]m[2]=-1}}}
Then
{{{(1/4)m[2]=-1}}}
{{{m[2]=-4}}}
You can use the point slope form of the line with slope=-4 and point (1,6).
{{{y-y[1]=m(x-x[1])}}}
{{{y-6=-4(x-1)}}}
{{{y=-4x+4+6}}}
{{{y=-4x+10}}}
{{{4x+y=10}}}
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We can verify the solution graphically.
{{{drawing( 300, 300, -20, 20, -20, 20,grid( 1 ),circle( 1, 6, .5 ),graph( 300, 300, -20, 20, -20, 20, (1/4)x-12, -4x+10)) }}}