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We do not usually see a line in this form, but it can be useful. Let $a=x\;intercept$. Let $b=y\;intercept.$ We know that $$slope=-b/a=\Delta y/\Delta x.$$ So the slope intercept form, written only with axes intercepts is $$y=\frac{-b}{a}x+b.$$ This can be rearranged to be $$\frac{x}{a}+\frac{y}{b}=1.$$