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3 years ago

What is the point slope equation of a line with slope -4 that contains the point (-2,7)?

Mathematics

2 answers:

BartSMP [9]3 years ago

7 0

Answer: $(y-7)=-4(x+2)$

Step-by-step explanation:

The equation of a line in point slope form with slope m and passing through point (a,b) is given by :-

$(y-b)=m(x-a)$

Given : The slope of the line : m= -4

The point from which line is passing : (a,b) =(-2,7)

Then , the point slope equation of a line with slope -4 that contains the point (-2,7) will be :-

$(y-7)=-4(x-(-2))\\\\\Rightarrow\(y-7)=-4(x+2)$

ad-work [718]3 years ago

3 0

Point slope form: (y-y1)=m(x-x1)

Answer:
(y-7)=-4(x+2)

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3 years ago

Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

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Step-by-step explanation:

Hello, please consider the following.

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So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

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Step 1 - for n = 1

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Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

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So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

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3 years ago