You can fix the cut by sanding an area about 4 to 6 inches to either side smooth out the area then skim over with a bit of drywall patch 'mud'. You can buy it already mixed in a small tub. Use a 4 inch wide putty knife and press a small amount with some force into the scratch. You can go over it a few times and scrape it away again to get some practice. It is important to know that the better you apply the mud the less sanding you will have to do after.
When the mud is dry, you will need a fine sanding block. The easiest way to make one instead of buying one is to fold a paper towel and lay it on a 8 to 10 inch piece of 2x4 and wrap sandpaper over the paper towel. The paper towel will act as a bit of cushion to push the paper out in the middle so you are not sanding with only the edges. You want to use fine to very fine sanding paper I think 220 grit is good.
Sand softly to blend the repair into the wall, look at it from the side to see if you left a lump of mud over the scratch, you can use a straight edge on the wall to check, but don't be too concerned because often the mud over the drywall seams isn't flat either.
As for the texture, it looks like the paint is more than one layer and was applied with a roller. Your patch will only have one layer and will be smoother than the rest of the wall. if you paint the patch first, let it dry then go over it 2 more times it should blend in well. You could use a thicker paint that will show the roller marks better.