Answer:
f(x)=6x-5
Step-by-step explanation:
The common difference is 6 because of the following:
7-1=6
13-7=6
19-13=6
25-19=6
31-25=6
The common difference is the slope of the linear equation.
Slope-intercept form for a function is f(x)=mx+b where m is the slope and b is the y-intercept.
We just found m=6.
f(x)=6x+b
The y-intercept happens at x=0.
I'm referring to looking at the data as:
x | y
1 | 1
2| 7
3| 13
4| 19
5| 25
6| 31
We can use the pattern that y goes up by 6 as x goes up by 1 to find what happens at x=0.
x| y
0 1-6=-5
So b=-5.
So the function that we are looking for is f(x)=6x-5.
