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 \ (-2y)/(-2)=(3)/(-2)-(x)/(-2)`


`(-2y)/(-2) \ \textgreater \ \mathrm{Apply\:the\:fraction\:rule}:\ (-a)/(-b)=(a)/(b) \ \textgreater \ (2y)/(2)`


`\mathrm{Divide\:the\:numbers:}\:(2)/(2)=1 \ \textgreater \ y`


`(3)/(-2)-(x)/(-2) \ \textgreater \ \mathrm{Apply\:rule}\:(a)/(c)\pm (b)/(c)=(a\pm \:b)/(c) \ \textgreater \ (3-x)/(-2)`


`\mathrm{Apply\:the\:fraction\:rule}:\quad (a)/(-b)=-(a)/(b)\ \textgreater \ -(-x+3)/(2) \ \textgreater \ y = -(3-x)/(2)`


`Therefore... y=(1)/(2)x-(3)/(2) (Note: m=(1)/(2),\:b=-(3)/(2))`

M is the slope and b is the y intercept.

Hope this helps!