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Slope intercept form

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

Quote:

Originally Posted by grapesicle

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! (: