keeping in mind that parallel lines have the same exact slope, then hmmmm what is the slope of 2x+5y = 3 anyway?
[tex] \bf 2x+5y=3\implies 5y=-2x+3\implies y=\cfrac{-2x+3}{5}
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y=\stackrel{slope}{-\cfrac{2}{5}}x+\cfrac{3}{5}\impliedby \textit{slope-intercept form} [/tex]
so we're really looking for the equation of a line whose slope is -2/5 and runs through 2, -3,
[tex] \bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad \qquad \qquad
slope = m\implies -\cfrac{2}{5}
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\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-3)=-\cfrac{2}{5}(x-2)
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y+3=-\cfrac{2}{5}x+\cfrac{4}{5}\implies y=-\cfrac{2}{5}x+\cfrac{4}{5}-3\implies y=-\cfrac{2}{5}x-\cfrac{11}{5} [/tex]
