## Elementary Algebra

If a line has a negative slope, it means that the change in $y$ is negative when the change in $x$ is positive because $\text{slope}=\frac{\text{change in}\:y}{\text{change in}\:x}$This scenario would result in a negative divided by a positive, which would result in the desired negative slope. When we put this scenario into words, we find that when $x$ increases, we move from left to right, and when $y$ decreases, we move down. This means that, indeed, a line that has a negative slope falls when we move from left to right.