Answer:
[tex]f(x) = 7x + 30[/tex]
Step-by-step explanation:
We need at least two points to write the equation of a straight line.
The recursive formula that Elijah wrote is:
[tex]f(0) = 30[/tex]
[tex]f(n + 1) = f(n) + 7[/tex]
When we substitute n=0, we get:
[tex]f(0 + 1) = f(0) + 7[/tex]
[tex]f(1) = 30 + 7[/tex]
[tex]f(1) = 37[/tex]
The points (0,30) and (1,37) lies on this line.
The equation of this line is of the form:
[tex]f(x) = mx + b[/tex]
where b =30 is the y-intercept and m=7 is the slope.
We plug in these values to get:
[tex]f(x) = 7x + 30[/tex]
Note that the slope of the line is equal to the common difference of the Arithmetic Sequence.
You could also use the two points to find the slope:
[tex]m = \frac{37 - 30}{1 - 0} = 7[/tex]
