Question: "A line in the $xy$-plane contains the points $(5, 4)$ and $(2, –1)$. Which is bigger: a) the slope of the line or b) $0$."
Result: They draw out the figure and say "you can see that the line through the two points slants upward and to the right. So the slope of the line is greater than $0$.
Conflict: However, when I use the formula to find the slope:
Slope $=\frac{y_2-y_1}{x_2-x_1}$
The result I receive is $-1$.
Seeing your comment, you seem to fix a particular point as $(x_2,y_2)$. @prog_SAHIL was trying to tell you to recheck your calculations with the points you have already chosen, he was not telling you to fix a particular point as $(x_2,y_2)$.
You can choose any of the points as $(x_2,y_2)$ and the other as $(x_1,y_1)$.
If you take $(2,-1)$ as $(x_2,y_2)$, you get:
Slope $\displaystyle=\frac{y_2-y_1}{x_2-x_1}=\frac {(-1) -4}{2-5}=\frac{5}{3}$
Or
If you take $(5,4)$ as $(x_2,y_2)$, you get:
Slope $\displaystyle=\frac{y_2-y_1}{x_2-x_1}=\frac {4 -(-1)}{5-2}=\frac{5}{3}$ .