SOLUTION: I am driving on a highway at a constant speed. After I've been driving for 3 hours, I pass mile marker 210. Two hours later I pass mile marker 90. I want to consider where I am on

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I am driving on a highway at a constant speed. After I've been driving for 3 hours, I pass mile marker 210. Two hours later I pass mile marker 90. I want to consider where I am on       Log On


   

Question 768564: I am driving on a highway at a constant speed. After I've been driving for 3 hours, I pass mile marker 210. Two hours later I pass mile marker 90. I want to consider where I am on the highway (by mile marker) and how long I've been driving. What is the equation? The x/y intercept?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The equation relating position (mile marker) to time driving hours) is the equation of the line that contains points (3,210) and (5,90).
slope=%2890-210%29%2F%285-3%29=-120%2F2=-60
That is the speed (60mph), with a minus sign that means mile marker numbers are going down.
The equation in point-slope form, based on point ((5,90) is
y-90=-60%28x-5%29
(We could also have written it based on point (3,210) as
y-210=-60%28x-3%29
From either form of the equation we could convert it to the slope-intercept form by solving for y. That would be the equation most useful in this situation.
y-210=-60%28x-3%29-->y-210=-60x%2B180-->highlight%28y=-60x%2B390%29
The y-intercept is highlight%28390%29, the mile marker where the driving at constant 60mph speed started.
The x-intercept can be calculated by making y=0 in (any form of) the equation, and then solving for x.
For example, from the slope-intercept form,
0=-60x%2B390-->60x=390-->x=390%2F60-->x=13%2F2-->x=highlight%286.5%29
In other words, 6.5hours=6hours30minutes is the x-intercept, which means that the mile marker 0 will be reached after driving for that long.