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?

mathtoo May 16, 2018

#1**+2 **

**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=\(\boxed{41}\) **

tertre May 16, 2018

#2**+3 **

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

GYanggg May 16, 2018