# How to find the equation of a line

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

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)

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

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