Linear Equation Word Problems

Question

A meteorologist estimates that on a sunny day, the air temperature decreases by about 4 degrees fahreheit every 1,000 (ft) of elevation gain. On a certain day, the air temperature outside an airplane flying above Seattle is -58 degrees Fahrenheit and the ground level temperature in Seattle is 70 degrees fahrenheit. If x is the height above Seattle, in feet, at which the plane is flying, which of the following best models the situation?

Answer Choices:

A. 70=−4/1,000​x−58

B. 70=4/1,000​x−58

C. −58=−4x+70

D.−58=4x+70

Answer 1

Hello Mila,

You're told the air temperature decreases by 4 F for every 1000 ft of elevation, so your answer should have 4/1000 in it. C and D do not, so you can safely eliminate them. Just like that, you're down to A and B.

Remember a linear relationship is always represented as y = mx + b;

1. The phrase "the air temperature decreases by about 4 degrees fahreheit every 1,000 (ft) of elevation gain" tells you the variable y represents air temperature. Here, they give you an air temperature of -58 degrees Fahrenheit, so y = -58
2. m is the slope. Here it decreases, by 4 F for every 1000 ft, so it is NEGATIVE: m = -4/1000
3. x, as the problem says, is the height above Seattle at which the plane is flying
4. b is the y-intercept; in other words, it is the TEMPERATURE at ground level in Seattle. The problem says that temperature is 70 degrees Fahrenheit.

Plugging those numbers in y = mx + b gives us:

-58 = (-4/1000)*x + 70 which doesn't exactly look like A or B...yet!

Add (4/1000)*x to both sides and you get: (4/1000)*x - 58 = 70 which looks like B but let's rearrange it one last time by swapping both sides:

70 = (4/1000)*x - 58

Now it looks EXACTLY like B which is the right answer.