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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 $-1$.

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    $\begingroup$ recheck your calculations. $\endgroup$ – prog_SAHIL Sep 6 '18 at 4:48
  • $\begingroup$ @prog_SAHIL Thank you. I didn't realize the Y2 and X2 were the upper right-most points on the graph. $\endgroup$ – Daniel Connelly Sep 6 '18 at 4:52
  • $\begingroup$ $\frac {-1 -4}{2-5} = -1$??? $\endgroup$ – fleablood Sep 6 '18 at 5:24
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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 $\displaystyle=\frac{y_2-y_1}{x_2-x_1}=\frac {4 -(-1)}{5-2}=\frac{5}{3}$ .

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  • $\begingroup$ Yes. Thanks for correcting me. I need to go to sleep, I think. $\endgroup$ – Daniel Connelly Sep 6 '18 at 6:26
  • $\begingroup$ @DanielConnelly You are welcome and sleep well :) Try to learn more about cartesian coordinates and lines. You can start from here Cartesian - Wiki Lines - Geometry. $\endgroup$ – paulplusx Sep 6 '18 at 6:34

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