The point-slope form is preferable to the slope-intercept form when we don't care about the y-intercept. Suppose that the population of a city was 50,000 in the year 2010, and it increases by 1,000 every year. Then the population Y in year X is given by Y = 50,000 + 1,000*(X-2010). It would be inconvenient to write the equation as Y = 1,000*X - 1,960,000, because the y-intercept has no meaning in this context. Looking forward, the point-slope formula shows up in calculus as the equation of the tangent line to a curve, and it is further generalized to Taylor series.
It's simple, really. What information are you given?
You use the slope-intercept form when the problem/description gives you a starting point at t=0 or x=0 and a rate of change (slope).
You use the point-slope form when the problem/description gives you a starting point somewhere else, other than at the y-axis and a rate of change (slope).
You might use the general form if you were given the two intercepts.
I missed the strong connection to slope formula (y1 - y2) / (x1 - x2) = m until I saw how it was set up by Bowen Kerins (@bowenkerins, http://patternsinpractice.wordpress.com/) in the What is CME? Global Math Department Talk. Watch from 15:14 to about 18:45 to see what I mean: https://www.bigmarker.com/GlobalMathDept/25Feb14
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Julie
3/16/2014 12:06:57 pm
Point slope form is more efficient when you are trying to find the equation of a line. Before my students learn it, I have them find the slope, then find the y-intercept, then make the equation. With point-slope form you save a step. I have them derive the point-slope form from these steps mentioned above first, so they can see it is actually not "different", just written in a different way.