How come when -1/3x+y=8/3 is converted to slope intercept form it ends up being y=1/3x+8/3 and not y=8-x ? Sorry I about the fractions I'm not sure how to make them stand the right way...

by the way what I did was multiply -1/3x by 3 and did the same to 8/3... which made the -1/3 cancel and the denominator on the 8 cancel out too... leaving me with x+y=8... then I subtracted x from y and ended up with y=8-x

How come when -1/3x+y=8/3 is converted to slope intercept form it ends up being y=1/3x+8/3 and not y=8-x ? Sorry I about the fractions I'm not sure how to make them stand the right way...

Starting with


- \frac {1} 3 x + y = \frac 8 3


you can poceeed by adding 1/3 x to both sides:


- \frac {1} 3 x + y + \frac 1 3 x= \frac 8 3 + \frac 1 3 x \\
\cancel {- \frac {1} 3 x} + y + \cancel {\frac 1 3 x } = \frac 8 3 + \frac 1 3 x \\
y = \frac x 3 + \frac 8 3


Another approach - similar to what you did - is to multiply both sides by 3:


3( - \frac {1} 3 x + y) = 3 ( \frac 8 3) \\
-x + 3y = 8


Now you have to rearrange to get the y term by itself, and then divide by 3:


3y = 8 + x\\
y =\frac 8 3 \ + \frac x 3


Which agrees with the earlier result. The error you made is in not multiplying the y term by 3 when you multiplied the other terms by 3.

Thank you so much, now I understand how to approach this! (: