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

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) (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 and

So we have one point (6000,76)

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

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

Start with the slope formula.

Plug in , , , and

Subtract from to get

Subtract from to get

Reduce

So the slope of the line that goes through the points

and

is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 76 to both sides.

Combine like terms.

Simplify

So the equation that goes through the points

and

is

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

Note: just replace "x" and "y" with T and E
RELATED QUESTIONS
It is 76 degrees F at the 6000-foot level of a mountain, and 49 degrees F at the... (answered by ankor@dixie-net.com)

jonah is driving along a straight and level road towards a mountain. At some point, he... (answered by Alan3354)

It is 76°F at the 5,500-foot level of a mountain and 41°F at the 9,000-foot level of... (answered by Alan3354)

Bob is driving along a straight and level road straight toward a mountain. At some point... (answered by lwsshak3)

Bob is driving along a straight and level road straight toward a mountain. At some point (answered by mananth)

Bob is driving along a straight and level road toward a mountain. At some point on his... (answered by Boreal)

What is the difference in elevation between the top of a mountain 8,867 ft above sea... (answered by Fombitz)

Bob is driving along a straight and level road straight toward a mountain. At some point... (answered by stanbon)