i dont undeestand how to use the matrices to write the form, do I convert to a matrix?

The equation of line passing through (3,5) and (-2,7) using determinants is given by:
The equation of line in slope-intercept form is:
[tex]\begin{gathered} 2x+5y-31=0 \\ y=\frac{-2}{5}x+\frac{31}{5} \end{gathered}[/tex]Equation of line in standard form and general form is given by:
[tex]2x+5y-31=0[/tex]The equation of line in slope-point form is given by:
[tex]y-5=\frac{-2}{5}(x-3)[/tex]