The equation of the line passing through the points [tex] (x_1,y_1) [/tex] and [tex] (x_2,y_2) [/tex] is
[tex] \frac{x-x_1}{y-y_1} =\frac{x_2-x_1}{y_2-y_1} [/tex]. Here [tex] \frac{y_1-y_1}{x_2-x_1} [/tex] is the slope of the line.
Substituting numerical values,
[tex] \frac{x-2}{y+3} =\frac{4-2}{2+3} \\
\frac{x-2}{y+3} =\frac{2}{5} \\
5x-10=2y+6\\
5x-2y-16=0 [/tex]
The equation of the line in standard form is [tex] 5x-2y-16=0 [/tex].
