Question

1. use the pattern to answer the questions.

figure 1 figure 2 figure 3
three figures with purple squares
a. create a table showing the number of cylinders in a given step
b. write an equation to represent the number of cylinders (y) in a given step (x).
a. create a table showing the number of cylinders in a given step
x y
0 blank

Explanation:

Step1: Count cylinders in each figure

• Figure 1 (x=1): Count the purple squares (cylinders). Let's see: 1 (top) + 2 (middle) + 1 (bottom) = 4? Wait, no, looking at the image: Figure 1 has 4? Wait, no, let's re-examine. Figure 1: top 1, middle 2, bottom 1. Total 4? Wait, Figure 2: top 1, middle 3, bottom 2. Wait, no, maybe I miscounted. Wait, Figure 1: Let's count the squares. Figure 1: 1 (top) + 2 (middle row) + 1 (bottom) = 4? Figure 2: 1 (top) + 3 (middle row) + 2 (bottom) = 6? Figure 3: 1 (top) + 4 (middle row) + 3 (bottom) = 8? Wait, no, maybe the pattern is increasing by 2? Wait, Figure 1: 4, Figure 2: 6, Figure 3: 8. So the common difference is 2. So for x=1, y=4; x=2, y=6; x=3, y=8. Then for x=0 (step 0), we can find the y-intercept. The slope (m) is (6-4)/(2-1)=2. So the equation is y = 2x + b. Plug x=1, y=4: 4 = 2(1) + b → b=2. So for x=0, y=2(0)+2=2. So the table would be:

x	y
1	4
2	6
3	8

Step2: Verify the pattern

• The difference between consecutive y-values is 2 (6-4=2, 8-6=2), so the slope is 2. The y-intercept (when x=0) is 2, as calculated. So the table for part a (starting with x=0) has y=2 when x=0, y=4 when x=1, y=6 when x=2, y=8 when x=3.

Answer:

(for part a, x=0):
2