The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8200 ft, the liquid boils at 199.42°F. At an altitude of 4700 ft, the liquid boils at 206.07°F. Write an 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 2500 ft?
Write an equation.
b=nothing

Some real-life events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to build the model and predict unknown behaviors.

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

We are given the following points (H,A) where A is the altitude and P is the boiling point of a certain liquid: (8200,199.42) and (4700,206.07)

Applying the formula:

[tex]\displaystyle B-199.42=\frac{206.07-199.42}{4700-8200}(A-8200)[/tex]

Calculating:

[tex]\displaystyle B-199.42=\frac{6.65}{-3500}(A-8200)[/tex]

[tex]\displaystyle B-199.42=-0.0019(A-8200)[/tex]

[tex]\displaystyle B-199.42=-0.0019A+15.58[/tex]

[tex]\displaystyle B=-0.0019A+15.58+199.42[/tex]

The equation is:

[tex]\displaystyle B=-0.0019A+215[/tex]

Finally, we calculate the boiling point at A=2500 ft:

\displaystyle B=-0.0019*2500+215

B = 210.25°F

The boiling point of the liquid it 210.25°F