Question 800669
The description means two points on the line are (3,0) and (0,3/5).  


Apply the standard form equation for a line, {{{Ax+By=C}}}.


The point (3,0) means {{{A*3+B*0=C}}}
{{{3A=C}}}
{{{A=C/3}}}


The point (0,3/5) means {{{A*0+B(3/5)=C}}}
{{{B(3/5)=C}}}
{{{B=(5/3)C}}}


The slope will be negative, considering those two axes intercepts.  You should be able to algebraicly relate the standard form equation to the slope intercept form equation and see that {{{highlight(m=-(A/B))}}}, and you already have your "b", y-intercept.
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Compute the value for the slope, m.
{{{m=-(1/3)/(5/3)}}}
{{{m=-(1/5)}}}
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The equation for the line in slope-intercept form is then {{{highlight(y=-(1/5)x+3/5)}}}


You could convert that into standard form easily if you want.
{{{5*y=5(-(1/5)x+3/5)}}}
{{{5y=-x+3}}}
{{{highlight(x+5y=3)}}}



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Note, you can ignore "standard form" if you wish, and do everything according to definition of slope, and knowledge of slope-intercept equation form.  The two given axes intercepts give you enough information.
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