Question 882301
Same x-intercept.  Find that value using the given line.

{{{y=3x+1}}}
{{{3x+1=y=0}}}
{{{3x+1=0}}}
{{{3x=-1}}}
{{{x=-1/3}}}, so point is (-1/3, 0).


The other line, perpendicular, is {{{y=-(1/3)x+b}}}, NOT because of the x-intercept; but because you need 3*m=-1, the product of the slopes must be negative 1.  Now you still need to solve for b.
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{{{b=y-(-1/3)x}}}
Substitute the known point which is on both lines.
{{{b=0-(-1/3)(-1/3)}}}
{{{b=1/9}}}
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Wanted Equation:  {{{highlight(y=-(1/3)x+1/9)}}}.