When I was in school I learned that slope could be found with the following: $$m=\frac{y_2-y_1}{x_2-x_1}$$ When given the coordinates $(-3, 0)$ and $(0, 5)$, plotting these points on a Cartesian plane shows a positive slope, but using the slope equation: $$m=\frac{5-0}{0-3}$$ $$m=\frac5{-3}$$ where a positive divided by a negative is a negative value and thus negative slope.
I realize the correct slope is $\frac53$. But why is the formula we learned in grade school breaking down here? Am I making some obvious mistake or what? I'm trying to help a young student with Algebra and I'm not sure how to explain how I arrive at $\frac53$ other than "I just know". Help is appreciated.
You copied the sign incorrectly; the correct calculation is $$m=\frac{5-0}{0-(-3)}=\frac53$$