If we see an equation in the form y=mx+c (where m and c are just some numbers), but the important thing is that the left hand side is "y" and not "2y" or "3y", then the m is the slope.
So y=5x+7 has a slope of 5 (the number before the x) And y=2x+7 has a slope of 2 (the number before the x)
So as you move from left to right, the one with greater slope will increase y value faster. Just like if you were climbing two mountains. If you went for 1 kilometre up a really steep mountain, you would be higher up than if you went for 1 kilometre up a less steep mountain.
Another way of saying this is that by changing an equation from slope 5 (steep) to slope=2 (less steep), then "It will increase at a slower rate than before"
