A constant rate of change of $\frac{3}{2}$ through $(0,1)$ means a straight line with slope $\frac{3}{2}$ and $y$-intercept $1$.

The graph must be a line (not a curve) passing through $(0,1)$ going up with slope $\frac{3}{2}$.

Choice G shows a straight line through $(0,1)$ with positive slope.