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quick help!..

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When x=1, y=5, when x=2, y=9, when x=3, y=13, and so on. What is the value of y, when x=10? May 16, 2018

#1
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When x=1, y=5, when x=2, y=9, when x=3, y=13, and so on. What is the value of y, when x=10?

Solution:

We know that the difference between y and x is 4, as we can see in our pattern. But, if we look more closely, we can see that 4x+1=y. (1*4+1, 2*2+1=5, 3*4+1=13, and so on). So, to find y when x=10, we simply do 4(10)+1=$$\boxed{41}$$  .
May 16, 2018
#2
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There is a more reliable way to do this.

We notice that these can be expressed as points of a line,

$$(1,5);(2,9);(3,13)...$$

We can treat this as a function problem, and we need to solve for the equation of the line.

You first find the slope.

$$\frac{9-5}{2-1}=4\\ y=4x+b\\ 5 = 4\cdot1+b\\ b=1$$

The equation of the line is $$y=4x+1$$

Now we plug in x = 10,

$$y = 4\cdot10+1=\boxed{41}$$

I hope this helped,

Gavin

May 16, 2018
#3
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Hmm, that way is a bit more confusing.  tertre  May 16, 2018
#4
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Both x and y form an arithmetic series. Use the nth term formula to find the value of y when x = 10

nth term =F + (N - 1)*D, where F=First term, N = Number of terms, D =Common difference

10th term = 5 + (10 - 1)*4

= 5 + (9*4)

= 41

May 16, 2018