Given
An airplane has room for 300 coach- fair seats.
It can replace any 3 coach seats with 2 first class seats.
To proof
let coach seats = x
first class seats =y
As given in the question airplane has room for 300 coach- fair seats
i.e their is no first class seat.
First point becomes (300,0 )
replace 3 coach seats with 2 first class seats (Given in question )
second point becomes (297,2 )
we get two points (300,0 ) and (297,2 ) .
FORMULA
Equation of line with two point
[tex](y-y_{1})= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})[/tex]
put the points value in the above equation
[tex](y-0)= \frac{2-0}{297-300}(x-300)[/tex]
[tex]y = \frac{2}{-3} (x-300)[/tex]
sloving the above equation
we get the equation
[tex]y = \frac{-2}{3} x + 200[/tex]
Proof of (A)
Given : y=0
find the value of x
put this value in
[tex]y = \frac{-2}{3} x + 200[/tex]
we get
[tex]\frac{2}{3} x = 200[/tex]
x = 300
Proof of (B)
Given : x =0
find out the value of y
put these value in the equation
[tex]y = \frac{-2}{3} x + 200[/tex]
y = 200
Proof of (C)
Show that y is a linear function of x.
y is a linear function of x this is shown in the table and graph given below.
Proof of (D)
find a formula for y in terms of x
the equation
[tex]y = \frac{-2}{3} x + 200[/tex]
Hence proved
