Luke says you can always add and always multiply to join groups. Is he correct?
2 answers:
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We can observe that the function describing the graph is linear and so the equation is of linear nature:
Numbers m and n have special names. m is called the slope, n is called y-intercept.
From the graph one can tell that the line intercepts y-axis at y = -1 that means n = -1. What about the slope you say?
The slope can be calculated using two points' coordinates that lie on the line:
Now our line has an equation,
Hope this helps.
A
this is a geometric sequence since there exists a common ratio r between the terms
r = =
=
= 3
B
to obtain the next term in the sequence multiply the previous term by 3
= 3
← recursive rule
C
the n th term of a geometric sequence is
=
where is the first term in the sequence
= 7 ×
← explicit rule