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The equation for a line forms a part of my physics work.

The equation is: Y = mx+b

To refresh myself, I watched the following video on the formula. However, at 3:15 I went off in the wrong direction when I tried to get variable b by itself. I understand it works the teacher's way, but: why am I not allowed to -b from both sides, and then -6 from both sides?

When I continued doing it my potentially incorrect way, my answer became b=-2 which was correct, aside from the wrong sign as it should be positive.

It might have also been possible to have divided by 6 on both sides, but then the answer would become b=4/6 which is a decimal number not close to the correct answer.

I feel that little bits of missing knowledge are holding me back.

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  • $\begingroup$ It would be good if you showed the steps you took to find $b=-2$. That way you could receive more useful feedback. $\endgroup$
    – anonymous
    Commented Jan 7, 2021 at 2:13
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    $\begingroup$ I'm voting to close this question because - despite being a part of your physics study - this is a question about mathematics, not physics. It would be more at home on MathSE . $\endgroup$
    – J. Murray
    Commented Jan 7, 2021 at 2:16
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    $\begingroup$ @lee Voting to close because a question belongs on a different site is a vote to migrate. See here. $\endgroup$
    – J. Murray
    Commented Jan 7, 2021 at 3:40
  • $\begingroup$ Sorry, I wasn't aware of that. $\endgroup$
    – lee
    Commented Jan 7, 2021 at 3:57
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    $\begingroup$ This question failed migration because the asker is currently blocked from asking question on math.SE. Please do not ask questions here just because you're blocked from asking them on the site where they actually belong, this will only get you blocked on our site as well. $\endgroup$
    – ACuriousMind ♦
    Commented Jan 7, 2021 at 17:19

1 Answer 1

Reset to default
-1
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Teacher's way:

$\quad y=mx+b$

$\quad6=(\frac{1}{2})8 + b$

$\quad6=4 + b$

$\,-4\,-4$

$\quad2= b$

Your way (-b, -6, fixed):

$\quad y=mx+b$

$\quad6=(\frac{1}{2})8 + b$

$\quad6=4 + b$

$\,-b\qquad-b$

$\quad6-b=4$

$\,-6\qquad-6$

$\,-b=-2$

$\quad b=2$

Your way (-b, divide by 6, gets stuck):

$\quad y=mx+b$

$\quad6=(\frac{1}{2})8 + b$

$\quad6=4 + b$

$\quad\frac{6}{6}=\frac{4+b}{6}$ (stuck)

OR

$\quad6=4 + b$

$\,-b\qquad-b$

$\quad6-b=4$

$\quad\frac{6-b}{6}=\frac{4}{6}$ (stuck)

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  • 2
    $\begingroup$ You're not actually changing anything, those are equivalent. $-b = -2$ so $ (-1)b=(-1)2$, thus $b=2$. $\endgroup$
    – Monopole
    Commented Jan 7, 2021 at 2:40
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    $\begingroup$ @securityauditor that's exactly it $\endgroup$
    – J Kusin
    Commented Jan 7, 2021 at 2:50
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    $\begingroup$ Exactly, you can divide both sides by -1. Or you can multiply both sides by -1 then again you will get $b=2$. $\endgroup$
    – Monopole
    Commented Jan 7, 2021 at 2:52
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    $\begingroup$ You have $-b = -2$ and if you multiply or divide this equation by -1 (or any finite, non-zero number), you don't change anything b is still gonna be 2. $\endgroup$
    – Monopole
    Commented Jan 7, 2021 at 3:02
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    $\begingroup$ It's quite easy @securityauditor. For example: If $2a=2b$, you can divide both sides by 2 to get $a=b$. That doesn't change anything. It's called the "multiplication and division property of equality" which states that if you multiply or divide both sides of an equation by the same number, then both sides are still equal. I suggest you to learn these(and other properties of equality) on google as this site is meant for question and answers that have got something to do with physics. $\endgroup$
    – lee
    Commented Jan 7, 2021 at 3:52

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