Question

3
consider the two patterns described below.

pattern\trule\tstarting number
x\tmultiply by 7\t1
y\tmultiply by 6\t1

which of the following coordinate pairs shows the two patterns?
a. (1,1) ; (6,7) ; (36,49) ; (216,343)
b. (1,1) ; (7,6) ; (49,36) ; (343,216)
c. (1,1) ; (7,6) ; (14,12) ; (21,18)
d. (1,1) ; (6,7) ; (12,14) ; (18,21)

Explanation:

Step1: Generate Pattern x terms

Start with 1, multiply by 7 each time:
$1$
$1 \times 7 = 7$
$7 \times 7 = 49$
$49 \times 7 = 343$

Step2: Generate Pattern y terms

Start with 1, multiply by 6 each time:
$1$
$1 \times 6 = 6$
$6 \times 6 = 36$
$36 \times 6 = 216$

Step3: Match to coordinate pairs

Combine terms as (x,y): $(1,1); (7,6); (49,36); (343,216)$

Answer:

B. (1,1) ; (7,6) ; (49,36) ; (343,216)