Answer:
Let y represents the number of gallons of fertilisers obtained by mixing x tsp of powder fertiliser
Given,
The number of gallons of liquid fertiliser by mixing 8 tsp of powder fertiliser = 5,
So, the number of gallons of liquid fertiliser by mixing 1 tsp of powder fertiliser = \(\frac{5}{8}\),
∴ the number of gallons of LF by mixing x tsp of powder fertiliser = \(\frac{5}{8}x\)
\(\implies y =\frac{5}{8}x\)
Which is the required equation.
Since, in the equation, for every distinct value of x there are distinct value of y,
Thus, the above relation is a function.
By the table,
x 1 2 3 4 5
y 5/8 5/4 15/8 5/2 25/8
It is clear that for each input value there are distinct output value,
\(y=\frac{5}{8}x\) is a function,
Now, by graphing,
It is clear that the equation \(y=\frac{5}{8}x\) follow the vertical line test,
That is, it is a function.
