The standard form of the equation of a line:
[tex]Ax+By=C[/tex]
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[tex]y+7=-\dfrac{2}{5}(x-10)\qquad|\text{use distributive property}\\\\y+7=-\dfrac{2}{5}x+\left(-\dfrac{2}{5}\right)(-10)\\\\y+7=-\dfrac{2}{5}x+2\cdot2\\\\y+7=-\dfrac{2}{5}x+4\qquad|\text{multiply both sides by 5}\\\\5y+35=-2x+20\qquad|\text{add 2x to both sides}\\\\2x+5y+35=20\qquad|\text{subtract 35 from both sides}\\\\2x+5y=-15[/tex]
