Question

rewrite the standard form equation below into slope-intercept form. x-2y=3 A. y=x+3 By=-3/2x-1/2 C.y=3/2x-1/2 D.y=1/2x-3/2

Answer 1

Let us start converting!

$x-2y=3 \ \textgreater \ \mathrm{Subtract\:}x\mathrm{\:from\:both\:sides} \ \textgreater \ x-2y-x=3-x$

$-2y=3-x \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}-2 \ \textgreater \ \frac{-2y}{-2}=\frac{3}{-2}-\frac{x}{-2}$

$\frac{-2y}{-2} \ \textgreater \ \mathrm{Apply\:the\:fraction\:rule}:\ \frac{-a}{-b}=\frac{a}{b} \ \textgreater \ \frac{2y}{2}$

$\mathrm{Divide\:the\:numbers:}\:\frac{2}{2}=1 \ \textgreater \ y$

$\frac{3}{-2}-\frac{x}{-2} \ \textgreater \ \mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c} \ \textgreater \ \frac{3-x}{-2}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\ \textgreater \ -\frac{-x+3}{2} \ \textgreater \ y = -\frac{3-x}{2}$

$Therefore... y=\frac{1}{2}x-\frac{3}{2} (Note: m=\frac{1}{2},\:b=-\frac{3}{2})$

M is the slope and b is the y intercept.

Hope this helps!