Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
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: $$(y-y_1)=m(x-x_1)$$

So it depends on what you already know

share|cite|improve this answer

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).

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.