The slope-point form of a line:
[tex]y-y_0=m(x-x_0)[/tex]
The slope-intercept form of a line:
[tex]y=mx+b[/tex]
1.
[tex]m=6,\ (4,\ 1)\to x_0=4,\ y_0=1[/tex]
Substitute
[tex]y-1=6(x-4)\qquad|\text{use distributive property}\\\\y-1=6x-24\qquad|\text{add 1 to both sides}\\\\\boxed{y=6x-23}[/tex]
2.
[tex]m=-5,\ (6,\ -3)[/tex]
Substitute
[tex]y-(-3)=-5(x-6)\qquad|\text{use distributive property}\\\\y+3=-5x+30\qquad|\text{subtract 5 from both sides}\\\\\boxed{y=-5x+24}[/tex]
3.
[tex]m=-\dfrac{1}{2},\ (-8,\ 2)\\\\y-2=-\dfrac{1}{2}(x-(-8))\\\\y-2=-\dfrac{1}{2}(x+8)\\\\y-2=-\dfrac{1}{2}x-4\qquad|\text{add 2 to both sides}\\\\\boxed{y=-\dfrac{1}{2}x-2}[/tex]
4.
[tex]m=0,\ (-7,\ -1)\\\\y-(-1)=0(x-(-7))\\\\y+1=0\qquad|\text{subtract 1 from both sides}\\\\\boxed{y=-1}[/tex]
