500g of pasta flour
1 pinch of salt
6 egg yolks, lightly beaten
4 eggs, lightly beaten
25ml of olive oil
I cannot help thinking that whoever tries to use that recipe (which is from a reputed source) will only be met with failure, unless the point is to make weird pancakes.
Some of you may have been making pasta with me at some point, some might have been inspired in trying to go it alone using this recipe and some might be intrigued by the whole issue for the first time this once. Whatever the situation, the point I am trying to make is that when traditional recipes from all around northern Italy call for 1 medium egg for each 100g flour (plus or minus a bit of salt or a dash of olive oil), it is not difficult to visualise a batter taking shape rather than a dough if using the recipe above. How is one going to use a pasta machine to roll the batter is frankly beyond comprehension. Do people actually use the recipes they write up?

And now onto a couple of points regarding fresh pasta which may help with understanding the differences between fresh pasta types. In Italy two main types of wheat are cultivated: durum wheat in the South, characterised by a warm yellow colour and coarser texture when milled, and normal wheat in the North, characterised by a white colour and a soft, almost impalpable texture of the flour obtained. What I the UK is known as plain flour is the equivalent of Italian 'soft wheat' which gives type 00, type 0, type 1 etc flour based on how refined the final product is, with 00 being the whitest.
Durum wheat has very high protein content which means that simply adding water and mixing with strength one obtains a gluten rich, plastic dough which can be shaped easily. This is why most southern Italian pastas are made simply mixing fine semolina with water and then shaped in characteristically small shapes which hold even during cooking in hot water. Pasta sheets are rather uncommon in the South.
Conversely in the North the gluten poor flour needs the proteins from eggs in order to get a dough which can be rolled into sheets (alternatively hot water should be used, like when making Asian noodles, but this is another story). With the addition of eggs the pasta will hold during cooking, much like the southern counterpart. It is the lecithin in the yolks which allows the pasta to become pliable and hold its shape, so theoretically we could make pasta just using the yolks and discarding the whites. Yet, pasta was originally a peasant food and nothing would be wasted, so the traditional way of making pasta is to add the entire egg. Nowadays restaurants looking to obtain a richer pasta will use a higher proportion of yolks to whites in making pasta, but I find it is not necessary, unless you plan on making a pavlova for pudding!
Enough of me blabbing. One last thing about making fresh egg based pasta: keep it harder than you think you'd like. After the resting time, when the gluten has relaxed, it will be remarkably softer than when you finished kneading it; and for some recipes and inspirartion, do have a look at the ones I have already posted.