The standard form:
[tex]Ax+By=C[/tex]
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (6, 1) and (5, 4). Substitute:
[tex]m=\dfrac{4-1}{5-6}=\dfrac{3}{-1}=-3[/tex]
[tex]y-1=-3(x-1)[/tex] use distributive property
[tex]y-1=-3x+3[/tex] add 1 to both sides
[tex]y=-3x+4[/tex] add 3x to both sides
[tex]\boxed{3x+y=4}[/tex]
