What is the boiling point of the liquid at 2600 feet

Question

the relationship altitude and the boiling point of a liquid is linear. At a atitude of 8500 feet. The liquid boils at 201.1 F. At an altitude of 4500 feet,the liquid boils at 206.42 F. Write a equation giving the boiling point b= of the liquid in degrees Fahrenheit in terms of altitude a, in feet. What is the boiling point of the liquid at 2600 feet

Answer 1

It's linear. So find the slope, with altitude as the x values and boiling point as the y values.

 

slope  =   (y₂ - y₁)/(x₂ - x₁)  =  (201.1 - 206.4)/(8500 - 4500)  =  -5.3/4000   =   -0.001325  (degrees F per ft.)

 

Now set up the Point/Slope form of the equation and convert it to the Slope/Intercept form.

 

  Y - 201.1   =  -0.001325 * (X - 8500)     Y  =  -0.001325 X  +  ( -11.2625 + 201.1 )  =  -0.001325 X + 189.8375.

 

Set X = 2600 and solve for Y.

 

 Oops; a mistake   It should be  Y  =  -0.001325 X  +  ( +11.2625 + 201.1 )  =  -0.001325 X + 212.3625.

Answer 2

Pretty,

       First, we will have to calculate the slope of the line, since this is a linear equation.

 

"a" in this problem is our dependent variable, like x.  "b" is our dependent variable, like y.

 

m = (201.1 - 206.42)/(8500 - 4500) = -0.00133

 

Next, we find the y-intercept by substituting the slope and the point (8500,201.1)

 

201.1 = -0.00133(8500) + y-intercept  ( I chose not to use b for this because we already have a variable called b)

 

212.405 = y-intercept.

 

So, the equation of the line in slope-intercept form is  b = -0.00133a + 212.405

 

Now we will substitute a = 2600 into the equation and solve for b.

 

b = -0.00133 * 2600 + 212.405 = 208.95

 

So, at an altitude of 2600 feet, water boils at 208.95⁰F.

 

Hope this helps.

 

Gordon