Question 176418
Parallel lines have slopes that are identical. 
Your first line is in slope-intercept form.
{{{y = (2/3)x-2}}}
Its slope is 2/3.
To find the equation of the second line, use the point-slope form of a line,
{{{y-y[p]=m(x-x[p])}}}
{{{y-1=(2/3)(x-2)}}}
Re-arrange the equation to slope-intercept form,
{{{y=(2/3)x-4/3+1}}}
{{{y=(2/3)x-1/3}}}
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Graph the lines to verify the solution.
{{{drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),circle( 2, 1, .2 ), graph( 300, 300, -5, 5, -5, 5, (2/3)x-2, (2/3)x-1/3)) }}}