Question

1. how many blocks would be in the 6th pattern2. how many blocks would be in the 77th pattern3. what pattern number would have 247 blocks4. what is the linear equation for this pattern5. where do you see your slope in the pattern6. where do you see your y-intercept in the pattern

Answer 1

We have the following:

The first thing is to calculate the equation for the pattern, which would be the following

$\begin{gathered} a_n=a_1+d\cdot(n-1) \\ a_1=4 \\ d=3 \\ \text{ replacing} \\ a_n=4+3\cdot(n-1) \end{gathered}$

Therefore:

1. how many blocks would be in the 6th pattern

$\begin{gathered} a_6=4+3(6-1) \\ a_6=19 \end{gathered}$

2. how many blocks would be in the 77th pattern

$\begin{gathered} a_{77}=4+3(77-1) \\ a_{77}=232 \end{gathered}$

3. what pattern number would have 247 blocks

$\begin{gathered} 247=4+3(n-1) \\ 3(n-1)=247-4 \\ n-1=\frac{243}{3} \\ n=81+1 \\ n=82 \end{gathered}$

4. what is the linear equation for this pattern

$\begin{gathered} y=4+3\cdot(x-1) \\ y-4=3(x-1) \\ or \\ y=3x+1 \end{gathered}$

5. where do you see your slope in the pattern

$\begin{gathered} y-y_1=m\cdot(x-x_1) \\ \text{ where m is the slope, therefore},\text{ in this case:} \\ m=3 \end{gathered}$

6. where do you see your y-intercept in the pattern​

$\begin{gathered} y=4+3x-3 \\ y=3x+1 \\ y=mx+b \\ \text{where b is the y-intercept, therefore} \\ b=1 \end{gathered}$