Question

A line passes through the point (4,-2),(9,-8).Write an equation for the line in point-slope form. Then rewrite the equation in slope-intercept form

Answer 1

First find the slope of the line segment joining (4,-2) and (9,-8).  It is:
        -8+2       -6
m = -------- = ------
          9-4         5

Using slope-intercept form,   y = mx + b:

                                              -8 = (-6/5)(9) + b, or -8 = -54/9 + b.

Then b must be -8 = -54/9 + b.  Solve for b: 

-72    54        -18
----- - ----- = -------- = -2.  Then y = mx + b becomes y = (-6/5)x - 2 (slope-
   9      9           9              intercept form).

Point-slope form is y-k = m(x-h), where (h,k) is a point on the line.

Then   y - (-8) = (-6/5)(x-9).  This is in point-slope form.