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Can anyone help?

I have the following equation that is in point slope form: $$y-3 = {\textstyle{3\over11}}(x-4).$$ I now need to get this equation into THIS form: $$3x-11y = -21.$$

The first step is to do the multiplication on the right hand side to give this answer:

$\ \ \ \ y-3 = {3\over11}x - ({3\over11} \cdot 4)$.

Then to get the $y$ alone on the left, move the $3$ over giving:

$\ \ \ \ y = {3\over11}x - ({3\over11}\cdot 4) - 3$.

Then do the calculation on the right to give:

$\ \ \ \ y = {3\over11}x + 1.90909090$.

But how do I get rid of the fraction $3/11$? Plus the values don't seem like they will add up? Seems like a primary school question but I can't figure this out. Any help would be appreciated.

In case your wondering, I have taken this from a tutorial found here (in step 3 of the tutorial).

PS: sorry if tag is wrong but I did not know what to add it under

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Multiply both sides by 11. Or better yet, do that first as in Ronald's answer. Also, it's a bad idea to use decimal representations here... –  David Mitra Apr 2 '12 at 23:50
    
And, nice write up of the question! –  David Mitra Apr 2 '12 at 23:54

1 Answer 1

up vote 2 down vote accepted

A sensible option is to multiply each term by 11 at the start, to get rid of the fraction. (actually, we're multiplying each side of the equation by 11)

$$y-3 = \frac{3}{11}(x-4)$$

leads to:

$$11y - 33 = 3(x-4)$$

I think you can continue from there! Let me know if you need more help.

If you prefer, you can also do the same thing (multiply by 11) after the last line of your work.

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Thanks a million guys, this really helped me out a lot. –  Hans Moolman Apr 3 '12 at 0:13

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