Question

What is the equation of the line, first written in point-slope form and then written in slope-intercept form?

Answer 1

Point-slope form is
y - y1 = m(x - x1), where the (x1, y1) is one of the points.

First find the slope, which is change in y over change in x, or 
$m= \frac{x2-x1}{y2-y1}$
The example points
(x1, y1) and (x2, y2) are now
( 3, 21 ) and ( 6, 12 ).
$m= \frac{12-3}{6-21}= \frac{9}{-3} = -3$


Now plug the slope and one of the points into the formula
$y - y1 = m(x - x1) \\ y - 12 = -3(x-6)$

To write in slope-intercept form, y = mx + b, simply solve for y.
$y - 12 = -3x + 2 \\ y = -3x + 30$

Answer 2

Point Slope:
y-12=-3(x-6)

From there you can find the slope intercept form:

y-12=-3x+18
y=-3x+30