SOLUTION: ? write a function rule for the table: x f(x) -1 3 0 0 1 -3 2 -6 please explain

Algebra ->  Functions -> SOLUTION: ? write a function rule for the table: x f(x) -1 3 0 0 1 -3 2 -6 please explain       Log On


   

Question 29741: ? write a function rule for the table:
x f(x)
-1 3
0 0
1 -3
2 -6
please explain
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
(x,y)
A(-1,3)
B(0,0)
C(1,-3)
D(2,-6)
Find the slope (rise/run) of the points.
+%28y2+-+y1%29%2F%28x2+-+x1%29+
A to B +%283-0%29%2F%28-1-0%29+ = +3%2F-1+
B to C +%280--3%29%2F%280-1%29+ = +3%2F-1+
C to D +%28-3--6%29%2F%281-2%29+ = +3%2F-1+
all have the same slope so they lie on the same line.
use the point-slope formula:
+y+=+mx+%2B+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+%2B+b+
+0+=+-3%280%29+%2B+b+
+0+=+0+%2B+b+
+0+=+b+
now ... using the slope and the y-intercept ... substitute once more.
+y+=+mx+%2B+b+
+y+=+-3x+%2B+0+ or +y+=+-3x+
remeber ... f(x) is just a fancy way of saying y
+f%28x%29+=+-3x+