Write an equation for the given line:
1. P(2,3), m=2
2. P(1,0), no slope
3. P (-1,2), m=-1/2
4. P(2,3), m = 0
1.y=2(x-2)+3
2. y=(x-1)
3. y= -1/2(x+1)+2
4. y=(x-2)+3
The point-slope form of the equation to a line is given by $\displaystyle (y_2-y_1)=m(x_2-x_1)$.
The answer you have for the first problem is correct. In the second problem, however, your are asked to find the equation to a line that goes through the point $\displaystyle (1,0)$ that has no slope. No slope implies that the line is vertical. Thus, the equation is $\displaystyle x=1$.
Number 3 is correct.
Number 4 is wrong. If I use the formula that I have written at the beginning og this post, I have
$\displaystyle y-3=0(x-2)$
$\displaystyle y-3=0$
$\displaystyle y=3$
This is a horizontal line, as is expected given a slope of 0.