Question

Stephen is walking from his house to his friend Sharon's house. When he is 12 blocks away, he looks at his watch. He looks again when he is 8 blocks away and finds that 6 minutes have passed. Write 2 ordered pairs for these data in the form (time, blocks).
Write a linear equation for these 2 points.
What is the total amount of time it takes Stephen to reach Sharon's house? Explain please.

Answer 1

(time t, blocks d)
(0 , 12)
(6 , 8 )
d is distance from house in blocks
d = m t + b
12 = 0 + b so b = 12
8 = m *6 + 12
-4/6 = m
m = -2/3
so
d = -(2/3) t + 12
0 = -(2/3) t + 12
t = (3/2) * 12 = 18 minutes

Answer 2

the two ordered pairs from your information are
(0,12) and (6,8)

slope = (12-8)/-6
= -2/3

So Blocks = (-2/3)t + b
using (0,12)
12 = 0 = b
b = 12
so the linear equation is

Blocks = (-2/3)Time + 12

when he reaches Sharon's house Blocks = 0
so 0 = (-2/3)time + 12
(2/3)time = 12
time = 18

it will take 18 minutes