Find the slope of the line that passes through the two points (8, 5) and (10, 7).

Step-by-step solution

1. 1

   Assign the coordinates consistently. Slope is a difference of $y$ over the matching difference of $x$, so decide which point is first and keep that choice throughout:

   $(x_{1},y_{1})=(8,5),\qquad (x_{2},y_{2})=(10,7)$

2. 2

   Substitute into the slope formula.

   $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{7-5}{10-8}$

   Both coordinates are positive here, so there are no sign traps — the only risk is putting the $x$ difference on top.

3. 3

   Compute the rise and the run. The numerator is the rise and the denominator is the run:

   $\text{rise}=7-5=2,\qquad \text{run}=10-8=2$

4. 4

   Divide to get the slope.

   $m=\frac{2}{2}=1$

5. 5

   Interpret the result geometrically. A slope of exactly $1$ means the line climbs one unit for each unit it moves right, so it is parallel to the line $y=x$ and meets the $x$-axis at $45^{\circ}$. Reversing the labels gives $\dfrac{5-7}{8-10}=\dfrac{-2}{-2}=1$, confirming the value is independent of which point you call first.