Question

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

Answer 1

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.