Question

Heather wants to increase the time she jogs each week by 6 minutes. she is already able to jog for 10 minutes. the time heather jogs each week is given by the linear function f(x) = 6x + 4. which explicit rule is equivalent to this linear function?

Answer 1

The explicit rule would be 

$a_n=10+6(n-1)$.

This equation is in slope-intercept form, f(x)=mx+b.  This means the slope, m, is 6.  This tells us the rate of change of the line.  This corresponds to the common difference, d, of the sequence.

An explicit rule for this sequence is of the form

$a_n=a_1+d(n-1)$,

where a₁ is the first term and d is the common difference.  We know that d = 6:
$a_n=a_1+6(n-1)$

From the problem, we are told that she is starting out running for 10 minutes.  This is a₁:

$a_n=10+6(n-1)$