First, let's put the line equation in the form ax + by + c = 0:
[tex]\begin{gathered} y=x-3 \\ x-y-3=0 \\ (a=1,b=-1,c=-3) \end{gathered}[/tex]Now, to find the distance to a point (x1, y1), let's use the formula:
[tex]\begin{gathered} d=\frac{|ax1+by1+c|}{\sqrt[]{a^2+b^2^{}}} \\ (2,3)\colon \\ d=\frac{|1\cdot2+(-1)\cdot3+(-3)|}{\sqrt[]{1^2+(-1)^2}} \\ d=\frac{|2-3-3|}{\sqrt[]{2}} \\ d=\frac{|-4|}{\sqrt[]{2}}=\frac{4}{\sqrt[]{2}}=\frac{4\sqrt[]{2}}{2}=2\sqrt[]{2}=2.83 \end{gathered}[/tex]So the distance is 2.83.
