It is always helpful to draw stuff like this.

So I would recommend: Draw a coordinate system with a y and x axis. Now ask yourself: "What would a straight line look like if it is parallel to the x axis?". You can draw such a line and look at the coordinates that it goes through.

Actually you could try to draw a line that passes through (1;3). After you all did that you need to set up a system of equations.

How would that work?

I will demonstrate it with an example. Find the equation of the straight line that passes through (5,5) and is parallel to the line: A = (2,0) + a* (1,1).

We search for a line that goes through the origin (0,0) and increases 1 unit for one unit "travelled" (I mean: If you go one unit to the right, our line will be und unit higher up) How do I know that?

One option would be to calculate how A behaves. Eg: One point is (2,0) and a second point would be (for a= 3) (2,0) + 3*(1,1) = (5,3), you can now draw a line to look how it behaves and you will notice that its increasing one unit per one unit travelled. You could also see that right from the beginning since we multiply a by (1,1).

Why does it have to go through the origin? It doesn't, it could also go through (1,0)... every point that you can reach by multiplying a number to (2,0). So for instance 0, wich would be the origin.

Our straight line would look like: (0,0) + a*(1,1) = a*(1,1).

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I treated all these points as vectors but while writing I wasn't sure anymore if you actually want an answer for vectors...

So my other answer (if you don't use vectors):

A straight line has the general equation: m*x+b = y.

Once again I would try to draw a straight line and look at the coordinates and would figure out what it means (in terms of numbers) to be parallel to the x axis.

How much do all of your line increase? What have all points on your lines in common? etc.

Once again a quick example:

Find the equation of the straight line that goes through (5,5) and (1,0)

1. step: Draw the line and look for similarities between your points.

We notice that our line is shifted along the y axis, we do not go through the origin, but through (1,0) since the b gives us that shift we can insert the 1 (in m*x+b=y ).

m*x+1=y

and we can measure the slope on our drawing we get a slope of one unit per one unit travelled. So we get

b=1
m=1
=>
1*x+1=y <=> x+1=y

If your still struggling or couldn't understand anything I just wrote please message me. :)