Verified answer

[tex]\frac{x-x_{1}}{x_{2}-x_{1}} = \frac{y-y_{1}}{y_{2}-y_{1}}[/tex]

[tex]\frac{x+2}{4+2} = \frac{y-1}{7-1}[/tex]

[tex]\frac{x+2}{6} = \frac{y-1}{6}[/tex]

[tex]x+2 = y - 1[/tex]

[tex]x - y = -3[/tex]