What is the equation of the line with (1,0) and (6,6)?
1 answer:
Answer:
6x -5y = 6
Step-by-step explanation:
You can use the 2-point form of the equation of a line to find it.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (6-0)/(6-1)(x -1) +0
y = 6/5(x -1) . . . . . . point-slope form
y = (6/5)x -6/5 . . . . slope-intercept form
5y = 6x -6
6x -5y = 6 . . . . . . . standard form
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<h2>Answer with explanation:</h2>
We are asked to prove by the method of mathematical induction that:
where n is a positive integer.
- Let us take n=1
then we have:
Hence, the result is true for n=1.
- Let us assume that the result is true for n=k
i.e.
- Now, we have to prove the result for n=k+1
i.e.
<u>To prove:</u>
Let us take n=k+1
Hence, we have:
( Since, the result was true for n=k )
Hence, we have:
Also, we know that:
(
Since, for n=k+1 being a positive integer we have:
)
Hence, we have finally,
Hence, the result holds true for n=k+1
Hence, we may infer that the result is true for all n belonging to positive integer.
i.e.
where n is a positive integer.
