Question 29741
(x,y)
A(-1,3)
B(0,0)
C(1,-3)
D(2,-6)
Find the slope (rise/run) of the points.
{{{ (y2 - y1)/(x2 - x1) }}}
A to B {{{ (3-0)/(-1-0) }}} = {{{ 3/-1 }}}
B to C {{{ (0--3)/(0-1) }}} = {{{ 3/-1 }}}
C to D {{{ (-3--6)/(1-2) }}} = {{{ 3/-1 }}}
all have the same slope so they lie on the same line.
use the point-slope formula:
{{{ y = mx + b }}}  m = slope   b = y-intercept  x and y are the ordered pair.
using the slope (-3) and point B (0,0) ... substitute and find b.
{{{ y = mx + b }}}
{{{ 0 = -3(0) + b }}}
{{{ 0 = 0 + b }}}
{{{ 0 = b }}}
now ... using the slope and the y-intercept ... substitute once more.
{{{ y = mx + b }}}
{{{ y = -3x + 0 }}} or {{{ y = -3x }}}
remeber ... f(x) is just a fancy way of saying y
{{{ f(x) = -3x }}}