Finding the slope of a line, slightly confused by the answer

Question

(just for context, this is from a study booklet for a military test. I haven't done algebra in about 10 years. I googled around but was having trouble finding specific information about the below.)

I was always taught that the equation to find the slop was $\dfrac{y_2-y_1}{x_2-x_1}$, so I was very surprised to see the answer was done via $\dfrac{y_1-y_2}{x_1-x_2}$ (never seen it done this way before). Is this typical/accepted way of finding the slope? Also was surprised that $\dfrac{-7}{17} = \dfrac{7}{-17}$, but I guess I can see why that would be since the slope is going to be negative either way when you divide the numbers?

Answer 1

Algebraically, those formulas are the same: $$ \frac{y_1-y_2}{x_1-x_2}=\frac{-(-y_1+y_2)}{-(-x_1+x_2)}= \frac{-y_1+y_2}{-x_1+x_2}= \frac{y_2-y_1}{x_2-x_1} $$

The minus signs just cancel each other out. And here's what your slope is going to be:

$$ \frac{1-8}{4-(-13)}=\frac{-7}{4+13}=-\frac{7}{17} $$

Answer 2

It’s like asking $ -\Delta{y}$ over $-\Delta{x}$ which will obviously give the same result as the change over that same positive interval.