[tex]\begin{gathered} \text{rate of change = }\frac{y_2-y_1}{x_2-x_1} \\ \text{rate of change = slope = gradient} \\ -2y+3x=2 \\ -2y=2-3x \\ \text{divide through by -2} \\ y=\frac{2}{-2}-\frac{3x}{-2} \\ y=-1+\frac{3}{2}x \\ y=\frac{3}{2}x-1 \\ \text{ using the equation:} \\ y=mx+c \\ \text{where } \\ m=\text{slope or gradient } \\ \text{Therefore,} \\ slope\text{ or rate of change = }\frac{3}{2} \end{gathered}[/tex]
