# 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?

• 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

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: $$(y-y_1)=m(x-x_1)$$