Question

what is the linear equation in y=mx+b for this pattern

Answer 1

In the given figure the number of block are increase by 2

So, The expression show an series of Airthmetic sequence where nth term is express as:

$a_n=a_1+(n-1)d$

So, the rate of change in teh system is 2

Slope =2

The expresion in the y = mx +b

Here we get m = 2

So,

equation will be :

$\begin{gathered} y=\text{ 1+(x-1)}2 \\ y\text{ = (x-1)2 +1} \end{gathered}$

where x respresnt the number of pattern and y represnt the number of blocks.

Answer : Expression : y = 2(x-1) + 1