Question 78911
How do I write the equation of the line passing through (2, 10) and (0, 10)?

This is a very important question because (2,10) is where you are, and (0,10) is where the pot of gold is

My idea of (2,10) is that it is 2 steps to the right and 10 steps up from the center

and (0,10) is zero steps to the right and ten steps up from the center

These two points are both 10 steps up from the center, but they are separated by 2 steps horizontally

If I draw a line through them, it will be a horizontal line

Horizontal lines have slope zero.  The 'up'ness or the y coordinate does not change.  The x coordinate can go from minus timbuctu to plus timbuctu and y will still be 10 no matter what x does.  y is simply not listening to x.  It is ignoring x despite all of x's protestations.

The equation I would write for this line would be y=10

You can see here that x is not mentioned at all.  You can think of x in this situation as flailing and clamoring wildly for attention while the y variable sits discreetly ignoring it.  This can also be written as

y = 0x + 10

where the slope is 0, and in this expression the situation is much less dramatic, where the number zero sits sedately and tactfully moderating x's anguish at being ignored.  The zero beautifully sits there, round and full like the moon, telling us that x is worthy and just, and that it is being multiplied by a perfectly good number just like any other x.