The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
[tex](x_1,\ y_1)[/tex] - given point
[tex]m[/tex] - given slope
The standard form:
[tex]Ax+By=C[/tex]
[tex]y-y_1=m(x-x_1)[/tex] use distributive property
[tex]y-y_1=mx-mx_1[/tex] add [tex]y_1[/tex] to both sides
[tex]y=mx-mx_1+y_1[/tex] subtract [tex]mx[/tex] from both sides
[tex]-mx+y=-mx_1+y_1[/tex] change the signs
[tex]mx-y=mx_1-y_1[/tex]
