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Prove that f(x)=a x+b , where a , b are ...

Prove that `f(x)=a x+b ,` where `a , b` are constants and `a >0` is an increasing function on `Rdot`

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Here,
f(x)=a x+b
Let `x_1, x_2` in `R` such that `x_1< x_2`. Then,
`x_1< x_2`
`Rightarrow a x_1< a x_2[therefore a > 0]`
`Rightarrow a x_1+b < a x_2+b`
`Rightarrow f(x_1) < f(x_2)`
`therefore x_1< x_2`
...
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