The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8200 ?ft, the liquid boils at 204.34 degrees°F

Question

The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8200 ?ft, the liquid boils at 204.342 degrees°F. At an altitude of 4500 ?ft, the liquid boils at 209.15 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?

 

b=?

Answer 1

Great question! The key to this question is recalling the details of how linear equations work, and filling in any gaps in your knowledge of linear equations as you go. In this case, they gave us two points on the linear equation. Therefore, we can get a slope using the expression

(y₂ - y₁)/(x₂ - x₁) = (204.342 - 209.15)/(8200 - 4500) = -0.00129946

Thus, the equation we have for you thus far is y = -0.00129946x + b

Once you have this slope, you can get the equation by plugging in one of the two (x,y) coordinate pairs given to you. Plugging in the point (8200, 204.342) into the equation, we get

204.342 = -0.00129946*(8200) + b

I don't want to give you the rest of the work, but at this point, you can get it by yourself or reply if you have follow-up questions! Just simplify by multiplying, and add or subtract as necessary. Feel free to ask any additional questions you may have!