## The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8500 ​ft, the liquid boils at 199.95 degree

Question

The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8500 ​ft, the liquid boils at 199.95 degrees F. At an altitude of 4300 ​ft, the liquid boils at 205.41 degrees 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 2600 ​ft?
Write an equation.
(Use integers or decimals for any numbers in the​ expression.)

in progress 0
2 weeks 2021-09-10T11:53:35+00:00 1 Answer 0

b = -0.0013a + 211

Step-by-step explanation:

Since the relationship is linear, we can use a linear equation. The formula in slope-intercept form is .

As the question specifies to use a for altitude and b for boiling point, change the variables equation to

b is the boiling point.

m is the slope.

a is the altitude.

c is the y-intercept.

To find the slope, we can use the equation except x is a and y is b.

The sets of information given are:

8500 ​ft, the liquid boils at 199.95°  (This can be info set 1)

4300 ​ft, the liquid boils at 205.41°  (This can be info set 2)

Substitute the info sets into the equation. The subscripts mean which info set to get the numbers from.

m = -0.0013

Find the y-intercept by substituting m = -0.0013 and a random info set. I will use info set 1. Isolate c, the only variable.

b = ma + c

199.95 = (-0.0013)(8500) + c  <= Simplify

199.95 = -11.05 + c

199.95 + 11.05 = -11.05 + 11.05 + c  <=add 11.05 on both sides to isolate c

c = 211  <= y-intercept

Put the y-intercept and slope into the equation of a line:

b = ma + c

b = -0.0013a + 211 <= This is the equation for the problem.