Question

writing equations of lines from written descriptions
on - ramp
the smith family took a road trip from their home in georgia to disney world. they drove at a constant rate. when they left their home, they recorded the odometer on their car. after 8 hours of driving, the odometer read 50,832 miles. after 20 hours, the odometer read 51,696 miles.
which linear equation models the situation?
(y = 12x + 50,256)
(y = 72x + 50,256)
(y = 8x + 50,832)
i do not know the answer yet
(y = 72x + 51,696)

Explanation:

Step1: Find total distance driven

$\text{Total distance} = 51696 - 50832 = 864$ miles

Step2: Find driving speed (slope)

$\text{Speed} = \frac{864}{20-8} = 72$ mph

Step3: Find initial odometer reading

Let $b$ = initial odometer reading. Use $x=8$, $y=50832$:
$50832 = 72\times8 + b$
$b = 50832 - 576 = 50256$

Step4: Form linear equation

$y = 72x + 50256$

Answer:

$y = 72x + 50,256$