To obtain the equation of the line that passes through these points, you can first obtain the slope of the line, using the formula
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]
And then use the point-slope formula
[tex]y-y_1=m(x-x_1)[/tex]
So, in this case, you have
[tex]\begin{gathered} (x_1,y_1)=(3,1) \\ (x_2,y_2)=(6,6) \end{gathered}[/tex][tex]\begin{gathered} m=\frac{6-1}{6-3} \\ m=\frac{5}{3} \end{gathered}[/tex]
Now using the point-slope formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1=\frac{5}{3}(x-3) \end{gathered}[/tex]
Therefore, the correct answer is D.
[tex]y-1=\frac{5}{3}(x-3)[/tex]
