Question 1005617
Try to make use of the y-axis intercept of one of the equations.  Find a linear equation perpendicular to these two parallel lines.  Drawing the graphs on the three equations on the same coordinate system should give you a clearer idea of the strategy.


Does that help?

Here is a way to think through.

{{{graph(300,300,-4,4,-4,4,3x/5+2,3x/5-1)}}}



The line perpendicular to both of these and passing through  (0,2) is {{{y-2=-(5/3)(x-0)}}}, which when put into slope intercept form is {{{y=-(5/3)x+2}}}; not surprising.  This line intersects your line 1 and line 2.


{{{graph(300,300,-4,4,-4,4,3x/5+2,3x/5-1,-5x/3+2)}}}


What is the intersection point of line 2 and the line {{{y=-(5/3)x+2}}} perpendicular to it?
{{{-(5/3)x+2=(3/5)x-1}}}
{{{-(5/3)x-(3/5)x=-1-2}}}
{{{(5/3+3/5)x=3}}}
multiply bothsides by lcd of 15,
{{{25x+9x=45}}}
{{{34x=45}}}
{{{x=45/34}}}
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Now find y of the intersection
{{{y=(3/5)x-1}}}
{{{y=(3/5)(45/34)-1}}}
.
.
{{{y=-7/34}}}
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The intersection of line 2 and the perpendicular is  ( 45/34, -7/34).


Now, what is the distance between  (0,2)  and  ( 45/34, -7/34 )?
Use the Distance Formula.