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 (3, 0) and (6, -3). Substitute:
[tex]m=\dfrac{-3-0}{6-3}=\dfrac{-3}{3}=-1[/tex]
The point-slope form:
[tex]y-(-3)=-1(x-6)\\\\\boxed{y+3=-(x-6)}[/tex]
or
[tex]y-0=-1(x-3)\\\\\boxed{y=-(x-3)}[/tex]
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
From the second point-slope form we have slope-intercept form:
[tex]y=-(x-3)\\\\y=-x-(-3)\\\\\boxed{y=-x+3}[/tex]
