Let's begin by listing out the information given to us:
[tex]\begin{gathered} (x_1,y_1)=(3,2) \\ (x_2,y_2)=\mleft(0,3\mright) \end{gathered}[/tex]We will proceed by calculating the slope:
[tex]\begin{gathered} slope(m)=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{3-2}{0-3}=\frac{1}{-3}=-\frac{1}{3} \\ m=-\frac{1}{3} \end{gathered}[/tex]Next is to use the point-slope formula to find an equation for the line:
[tex]\begin{gathered} \mleft(y-y_1\mright)=m(x-x_1) \\ x_1=3,y_1=2,m=-\frac{1}{3} \\ y-2=-\frac{1}{3}(x-3)\Rightarrow y-2=-\frac{1}{3}x+1 \\ \text{Put like terms together, we have:} \\ y=-\frac{1}{3}x+1+2\Rightarrow y=-\frac{1}{3}x+3 \\ y=-\frac{1}{3}x+3 \end{gathered}[/tex]
