Linear function definition: a function that will create a straight line when graphed.
11 is not a linear function (not a straight line), but 12 is.
For the tables, you can either plot out the graph or just look at the number patterns. A linear function's numbers will always increase/decrease accordingly at a constant rate. For example, in 14, you notice that as x increases by 1, y decreases by 2. This means it is a linear graph.
In 13, as x increases by 1, the output y increases but at a different rate each time. It increased by 3 at first, then 5, then 7. Hence, it is not a linear function. What is it then? It is an exponential function.
Answer:
(7m + 63)/3x = k
Step-by-step explanation:
<em>m=3kx/7 - 9</em>
<u><em>add 9 to both sides:</em></u>
m+ 9 = 3kx/7
<u><em>multiply both sides by 7:</em></u>
7(m+9) = 3kx
<u><em>distribute the 7:</em></u>
7m+63 = 3kx
<u><em>divide both sides by 3x:</em></u>
<u>(7m + 63)/3x = k</u>
this is the answer and where the parentheses -8+(3-2)+7=-16
The third choice is appropriate.
an = 5 - 3(n - 1); all integers n ≥ 1
_____
This equation follows the form for the general term of an arithmetic sequence.
an = a1 + d(n - 1)
where a1 is the first term (corresponding to n=1), and d is the common difference. From the problem statement, a1 = 5 and d = 2 - 5 = -3.
4x^2-25= (2x)^2-5^2=(2x-5)(2x+5)
Used: a^2-b^2=(a+b)(a-b)
