# When finding the equation of a line.

When finding the equation of a line, how do you know whether to use the slope-intercept form or the point-slope form?

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What do you mean with "point slope form"? The lines defined as $P=tP_0$ $(P,P_0\in\mathbb R^2)$ are not the most general ones: they all pass through $0\in\mathbb R^2$ –  Avitus Aug 13 '13 at 19:16
If you are given the $y$-intercept, you know a point $(0,b)$ on the line, so it is a special case of point-slope. –  André Nicolas Aug 13 '13 at 19:17
I do not uderstand Op's notation: in "point-slope", does he mean something like I wrote above or...? Maybe a point and an angle (w.r.t. the positive x-axis)? –  Avitus Aug 13 '13 at 19:23
"point-slope" is usually used for the form $y-y_1=m(x-x_1)$, where $(x_1,y_1)$ is a given point on the line and $m$ is the slope. –  user84413 Aug 13 '13 at 21:23

## 2 Answers

It depends on what you are given. If you only have two points, then you want to use slope-intercept form $y=mx+b$ where: $$m=\frac {\Delta y}{\Delta x}$$

Where $\Delta y = y_2-y_1$ (same with x). Then the y intercept can be solved for knowing that it is when x = 0.

For point slope form, if you know the slope of the line, m, and 1 point $(x_1,y_1)$you can use: $$(y-y_1)=m(x-x_1)$$

So it depends on what you already know

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As Andre remarks above, the slope-intercept form is just a special case of the point-slope form.
If you already know the slope and y-intercept, then of course the slope-intercept form is easiest to use. Otherwise, though, I would recommend writing the equation in point-slope form first, and then simplifying to the slope-intercept form if the problem requires it (or you just want the equation in simpler form).

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