Write a function rule for the table?

x y
-1 -4
0 -3
1 -2
2 -1

1 Answer
May 25, 2018

Answer: #y=x-3#

Explanation:

First, we can see that the function for this table is linear since each time #x# increases by #1#, #y# also increases by #1#. (Note: In general, we can see that a function is linear when the slope #m=(y_2-y_1)/(x_2-x_1)# between each data set is constant.)

Since we have established that the function given is indeed linear, we can use either point-slope form or slope-intercept form to find the function rule. In this case, since we are given a y-intercept #(0,3)#, we will use slope-intercept form: #y=mx+b#, where #m# is the slope and #b# is the y-intercept

Our first step in this process will be finding the slope:
#m=(y_2-y_1)/(x_2-x_1)#

Since the function is linear, we can choose any two data points, but choosing a data point in which either #x# or #y# is #0# will simplify the calculations. So, we will use #(0,-3)# and #(1,-2)#. Plugging into the slope formula:
#m=(-3-(-2))/(0-1)=-1/-1=1#

Since we are given the y-intercept #(0,-3)# we can simply plug #b# into the slope-intercept form formula and we find the function rule:
#y=mx+b#

#y=1x-3#

#y=x-3#, which is our final answer