Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 10 gallons of fuel, the airplane weighs 2155 pounds. When carrying 42 gallons of fuel, it weighs 2331 pounds. How much does the airplane weigh if it is carrying 48 gallons of fuel?

Question

myininaya · Answer

f(10)=2155
f(42)=2331

so we can write an equation since we know two points
(10,2155) and (42,2331)

$$slope=m=\frac{2331-2155}{42-10}=\frac{ 176}{32}=\frac{88}{16}=\frac{22}{4}=\frac{11}{2}$$

so we have

y=mx+b is a line
and we know m

$$y=\frac{11}{2}x+b$$


we know a point on the line (10,2155)

$$2155=\frac{11}{2}(10)+b$$
$$b=2155-\frac{11}{2}(10)=2155-11(5)=2155-55=2100$$
so the linear equation is 
$$y=\frac{11}{2}x+2100$$

so to find the weight of the airplane using 48 gallons
we just plug in 48 into 
$$f(x)=\frac{11}{2}x+2100$$

myininaya · Answer

$$f(48)=\frac{11}{2}(48)+2100=11(24)+2100=2364$$

anonymous · Answer

The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 42 minutes of calls is $15.26 and the monthly cost for 94 minutes is $19.94  . What is the monthly cost for 82  minutes of calls?