Question

Question
Tomas is planning out a rail trail using a map with a marked grid. The head of the trail, which has an information kiosk, is located at (3, 0). He moves 1 unit east and 3 units north and places a pin at (4, 3) to represent the location of another information kiosk. He continues placing pins so that each pin is 1 unit east and 3 units north in relation to the previous pin. Which of the following points will have pins? Select all that apply.

A coordinate plane has an x-axis labeled East from 0 to 10 in increments of 1 and a y-axis labeled North from 0 to 10 in increments of 1.

(1 point)
Responses

(5, 6)

(5, 6)

(6, 8)

(6, 8)

(7, 10)

(7, 10)

(8, 17)

(8, 17)

(9, 18)

(9, 18)

(10, 21)

(10, 21)
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Answer 1

Pins are at (3+n, 3n) for integer n ≥ 0 (or y = 3x − 9). Checking each point:

- (5, 6): 6 = 3·5 − 9 → yes
- (6, 8): 8 ≠ 3·6 − 9 → no
- (7,10): 10 ≠ 3·7 − 9 → no
- (8,17): 17 ≠ 3·8 − 9 → no
- (9,18): 18 = 3·9 − 9 → yes
- (10,21): 21 = 3·10 − 9 → yes

So the points with pins are (5, 6), (9, 18), and (10, 21).