SOLUTION: It is 76F at 6000 ft level of a mountain, and 49F at 12000 ft level of the mountain. Write an equation to find the temperature T at an elevation E on the mountain. Also, determine

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: It is 76F at 6000 ft level of a mountain, and 49F at 12000 ft level of the mountain. Write an equation to find the temperature T at an elevation E on the mountain. Also, determine       Log On


   

Question 173333: It is 76F at 6000 ft level of a mountain, and 49F at 12000 ft level of the mountain. Write an equation to find the temperature T at an elevation E on the mountain. Also, determine the temperature at 7000 feet.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=elevation (in feet) and y=temperature (in Fahrenheit)


So at 6000 ft, the temperature is 76F, this means that x=6000 and y=76

So we have one point (6000,76)




So at 12000 ft, the temperature is 49F, this means that x=12000 and y=49

So we have one point (12000,49)


So let's find the equation of the line through the two points (6000,76) and (12000,49)


First let's find the slope of the line through the points and


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%2849-76%29%2F%2812000-6000%29 Plug in y%5B2%5D=49, y%5B1%5D=76, x%5B2%5D=12000, and x%5B1%5D=6000


m=%28-27%29%2F%2812000-6000%29 Subtract 76 from 49 to get -27


m=%28-27%29%2F%286000%29 Subtract 6000 from 12000 to get 6000


m=-9%2F2000 Reduce


So the slope of the line that goes through the points and is m=-9%2F2000


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-76=%28-9%2F2000%29%28x-6000%29 Plug in m=-9%2F2000, x%5B1%5D=6000, and y%5B1%5D=76


y-76=%28-9%2F2000%29x%2B%28-9%2F2000%29%28-6000%29 Distribute


y-76=%28-9%2F2000%29x%2B27 Multiply


y=%28-9%2F2000%29x%2B27%2B76 Add 76 to both sides.


y=%28-9%2F2000%29x%2B103 Combine like terms.


y=%28-9%2F2000%29x%2B103 Simplify


So the equation that goes through the points and is y=%28-9%2F2000%29x%2B103



So the equation that represents the temperature T at elevation E is


T=%28-9%2F2000%29E%2B103


Note: just replace "x" and "y" with T and E