If a function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by g(x) = αx+β,

We have,

A function $g=\{(1,1),(2,3),(3,5),(4,7)\}$ is described by $g(x)=\alpha x+\beta$

As, $g(1)=1$ and $g(2)=3$

So, $\alpha(1)+\beta=1$

$\Rightarrow \alpha+\beta=1 \quad \ldots \ldots(\mathrm{i})$

and $\alpha(2)+\beta=3$

$\Rightarrow 2 \alpha+\beta=3 \quad \ldots .(\mathrm{ii})$

$(\mathrm{ii})-(\mathrm{i})$, we get

$2 \alpha-\alpha=2$

$\Rightarrow \alpha=2$

Substituting $\alpha=2$ in $(\mathrm{i})$, we get

$2+\beta=1$

$\Rightarrow \beta=-1$