What formulas do you know for finding equations of lines? There are a couple of standard ones:
Point-slope. If you know a point $(a,b)$ through which the line goes and the slope $m$ of the line, then the equation of the line is given by $y-b = m(x-a)$.
Two-points. If you know two points $(a,b)$ and $(c,d)$ that are on the line, then:
- If $a=b$, the line is vertical, and the equation is $x=a$.
- If $a\neq b$, then the slope of the line is $m = \frac{\text{rise}}{\text{run}} = \frac{d-b}{c-a}.$ Now use the point-slope formula with $(a,b)$ and $m$.
Slope-intercept. If you know the slope $m$ and the $y$-intercept $(0,b)$, then you are actually in a "point-slope" situation, with the point $(0,b)$. So the equation is just $y-b=mx$, or $y=mx+b$.
The first problem, you know a point on the line and the slope of the line. The point-slope formula gives you exactly what you want.
In the second problem, you know a point, and you are implicitly told the slope: "parallel to the $x$-axis" means that the line has to be horizontal. What is the slope of a horizontal line?
Same in the third problem: "parallel to the $y$-axis" means the line has to be vertical. The equations of vertical lines are always of the form $x=k$ for some constant $k$. If the line has to go through $(2,-5)$ and be vertical, what is the equation?
And in the fourth problem, you are again given the slope implicitly: "parallel to $2x-4y=3$" means "having the same slope as $2x-4y=3$". Find the slope of the line $2x-4y=3$ and proceed form there.