Use the information about altitude and boiling point to find two points.
Equation: b=- 0.0018a +212 Boiling Point of Water: 207.5^(∘)F
Practice makes perfect
To begin, let's make sense of the given information. It is given that the temperature at which water boils depends on altitude. This means that altitude a is the independent variable, and boiling point b is the dependent variable. We can write the given information as coordinates.
Altitude 8000 feet, boiling point 197.6^(∘) F: (8000, 197.6)
Altitude 4500 feet, boiling point 203.9^(∘) F: (4500, 203.9)
We can write an equation of b in terms of a in slope-intercept form. We will begin by finding the slope of the line that connects the points by using our points.
The slope - 6.33500 means that for every 3500 feet higher in altitude the boiling point decreases by 6.3^(∘). We can simplify the expression of the slope more.
At this point, we have the following equation.
b=- 0.0018a +n
To determine n we can substitute any of the given points into the equation for a and b and solve for n. We arbitrarily choose to use the point (4500,203.9).
The y-intercept of 212 means that at an altitude of 0 feet the boiling point is 212^(∘). Our complete equation is as follows.
b=- 0.0018a +212
We can use the equation to determine the boiling point at an altitude of 2500 feet. To do this, we will substitute a=2500 into the equation and solve for b.
