# Finding the equation of a line

I'm using this formula to work out the equation of a line joining points $(1,5)$ and $(-9,2)$:

$$\frac{y-y_1}{y_2-y_1} = \frac{x-x_1}{x_2-x_1}$$

Like this:

$$\frac{y-5}{2-5} = \frac{x-1}{-9-1}$$

$$= \frac{y-5}{-3} = \frac{x-1}{10}$$

$$= y-5= -3\frac{x-1}{10}$$

$$= y-5= \frac{-3x-(-3)}{10}$$

$$= y= \frac{-3x + 3}{10} + 5$$

$$= y= \frac{-3x + 53}{10}$$

$$Answer: y= \frac{-3}{10}x + \frac{53}{10}$$

My book gives the answer as:

$$y= \frac{3}{10}x + \frac{47}{10}$$

I can't see what I'm doing wrong. Any help greatly appreciated.

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the gentleman is right but before asking try to solve it once more using a fresh sheet of paper and without referring to the last solution...really takes you along way :) – cornercoder Apr 6 '12 at 9:10
Thankyou, I'll do that in future. – bot_bot Apr 6 '12 at 9:11
You shouldn't use the equality sign between two equations as you did. Equations are not equal to each other. Use the equivalence symbol "$\iff$" instead. But your solution is otherwise nicely written; going back through it carefully, checking that each step is valid, would quickly reveal where the error is. – David Mitra Apr 6 '12 at 12:58