Answer
The common difference(2) is equal to the slope of the line in slope-intercept form.
Work Step by Step
You have the sequence 3,5,7,9. The A(1) is 3.Find the common difference:
5-3=2
7-5=2
9-7=2
Plug into recursive formula ($A^{n}$=$A^{n-1}$+d).The recursive formula is $A^{n}$=$A^{n-1}$+2
Plug into the explicit formula $a^{n}$=A(1)+(n-1)d:
y=3+(x-1)(2)
y=3+2x-2
y=2x+1
The recursive formula relates to the slope-intercept form because the common difference is equal to the slope of the slope-intercept form.
