Answer:
5;5 and 65; they are congruent
Step 1: Find the slope:

This gives you
, but we need to find b.
To find b, substitute in one (x,y) pair and it doesn't matter which one. I'll go with (4,-2):
![\begin{aligned}-2&=-\dfrac{3}{2}(4)+b\\[0.5em]-2&=-6+b\\[0.5em]4&=b\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D-2%26%3D-%5Cdfrac%7B3%7D%7B2%7D%284%29%2Bb%5C%5C%5B0.5em%5D-2%26%3D-6%2Bb%5C%5C%5B0.5em%5D4%26%3Db%5Cend%7Baligned%7D)
Now take that b-value and plug in into the slope-intercept form:

It's always a good idea to toss in the other x-value from the other point, to make sure it checks out.
Answer:
a) The table of values represents the ordered pairs formed by the elements of the sequence (
) (range) and their respective indexes (
) (domain):

1 6
2 11
3 16
4 21
5 26
b) The algebraic expression for the general term of the sequence is
.
c) The 25th term in the sequence is 126.
Step-by-step explanation:
a) Make a table of values for the sequence 6, 11, 16, 21, 26, ...
The table of values represents the ordered pairs formed by the elements of the sequence (
) (range) and their respective indexes (
) (domain):

1 6
2 11
3 16
4 21
5 26
b) Based on the table of values, we notice a constant difference between two consecutive elements of the sequence, a characteristic of arithmetic series, whose form is:
(1)
Where:
- First element of the sequence.
- Arithmetic difference.
- Index.
If we know that
and
, then the algebraic expression for the general term of the sequence is:

c) If we know that
and
, then the 25th term in the sequence is:


The 25th term in the sequence is 126.
Answer:
-11
Step-by-step explanation: