In slope intercept form, write the equation for the line that passes through the point (2,3) and the point (7,13).

First, Use the slope equation to find the slope of the line passing thru these two points:

m=rise/run

Here, the rise is 13-3, or 10, and the run is 7-2, or 5.  Thus, the slope, m, is 10/5, or 2:  m=2.

We want the slope-intercept form, so let's begin with its general form:

y=mx+b.  Substitute the slope 2 for m:  y=2x+b.  Now choose either of the given points.  Arbitrarily I am choosing (2,3).  Then x=2 and y=3.

Substituting these values into y=2x+b:    3 = 2(2) + b, or b= 3 -4, or b = -1.

Then the equation of this line, in slope-intercept form, is y = 2x - 1.