The standard form:
[tex]Ax+By=C[/tex]
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[tex]y-1=-\dfrac{1}{4}(x-6)[/tex] use distributive property
[tex]y-1=-\dfrac{1}{4}x+\dfrac{3}{2}[/tex] multiply both sides by 8
[tex]8y-8=-2x+4\cdot3[/tex]
[tex]8y-8=-2x+12[/tex] add 2x to both sides
[tex]2x+8y-8=12[/tex] add 8 to both sides
[tex]\boxed{2x+8y=20}[/tex]
