The slope of a line is "rise over run".
It's the change in rise divided by the change in run, or the change in y divided by the change in x.
If I said, "Everytime I go up 3 feet, I go to the right two feet." The slope of that path would be 3/2.
So if I said "I went on a journey on a coordinate plane. I remember touching two points along my path. First I touched (1,1). I also remember touching the point (7,4)." What was the slope of my path?
Slope is change in y over change in x.
So how much did my y change? The y went from 1 to 7. So my y changed 6 units.
How much did my x change? The x went from 1 to 4. So my x changed 3 units.
So the slope of my path would be 6/3. That reduces to 2/1 or just 2. So every 2 units I went up, I went to the right 1 unit.