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.

(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

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

To find the ordered pairs in the form (time, blocks), we can consider the initial position as (0 minutes, 12 blocks) and the position after 6 minutes as (6 minutes, 8 blocks).

The linear equation for these two points can be written using the slope-intercept form, y = mx + b, where y is the number of blocks, x is the time in minutes, m is the slope, and b is the y-intercept.

To find the slope (m), we can use the formula: m = (y2 - y1) / (x2 - x1). Plugging in the values, we get:
m = (8 - 12) / (6 - 0)
m = -4 / 6
m = -2/3

Using the slope-intercept form, the equation becomes:
y = (-2/3)x + b

To find the y-intercept (b), we can substitute the coordinates of one of the points into the equation. Let's use (0, 12):
12 = (-2/3)(0) + b
12 = b

Therefore, the linear equation for Stephen's journey is:
y = (-2/3)x + 12

To determine the total amount of time it takes Stephen to reach Sharon's house, we need to find where the equation intersects the x-axis, which represents the number of minutes it takes for Stephen to reach 0 blocks (Sharon's house).

Setting y (the number of blocks) equal to 0, we can solve for x:
0 = (-2/3)x + 12
(-2/3)x = -12
x = (3/2)(-12)
x = -18

This means it takes Stephen -18 minutes to reach Sharon's house. However, negative time does not make sense in this context. It suggests that the question might have an error or an inconsistency.