SOLUTION: It is 76 degrees F at the 6000-foot level of a mountain, and 49 degrees F at the 12000-foot level of a mountain. Write a linear equation to find the temperature T at an elsevation

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: It is 76 degrees F at the 6000-foot level of a mountain, and 49 degrees F at the 12000-foot level of a mountain. Write a linear equation to find the temperature T at an elsevation       Log On


   

Question 185353: It is 76 degrees F at the 6000-foot level of a mountain, and 49 degrees F at the 12000-foot level of a mountain. Write a linear equation to find the temperature T at an elsevation e on the mountain, where e is in thousands of feet.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It is 76 degrees F at the 6000-foot level of a mountain, and 49 degrees
F at the 12000-foot level of a mountain.
Write a linear equation to find the temperature T at an elevation e on the
mountain, where e is in thousands of feet.:
:
Find the slope using the slope formula: m = %28y2-y1%29%2F%28x2-x1%29
Assign the given values as follows
x1 = 6 (for 6000 ft); y1 = 76
x2 = 12(for 12000ft); y2 = 49
:
m = %2849-76%29%2F%2812-6%29 = %28-27%29%2F6 = -9%2F2
;
Use the point slope equation y - y1 = m(x - x1) so create the equation
y - 76 = -9%2F2(x - 6)
y - 76 = -9%2F2x - (-27)
y - 76 = -9%2F2x + 27 + 76
y = -9%2F2x + 103; is the equation
Using e and T
T = -9%2F2e + 103
:
A graph would look like this:
+graph%28+300%2C+200%2C+-10%2C+20%2C+-20%2C+120%2C+%28-9%2F2%29x%2B103%29+
where elevation is the horizontal and Temp is the vertical
;
Sorry for the initial screw-up here. Carl