Find the slope of the line that passes through the two points (2, -4) and (6, 4).

Step-by-step solution

1. 1

   Label the points before substituting. The slope formula subtracts coordinates, so the only way to avoid a sign error is to fix which point is which and stick to it:

   $(x_{1},y_{1})=(2,-4),\qquad (x_{2},y_{2})=(6,4)$

   Either assignment works — swapping them negates both numerator and denominator, leaving $m$ unchanged — but mixing them within one calculation does not.

2. 2

   Substitute into the formula.

   $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{4-(-4)}{6-2}$

3. 3

   Simplify the numerator, minding the double negative. Subtracting a negative adds:

   $4-(-4)=4+4=8$

   This is the step the problem is really testing. Reading it as $4-4=0$ would wrongly give a horizontal line.

4. 4

   Simplify the denominator and divide.

   $6-2=4\qquad\Longrightarrow\qquad m=\frac{8}{4}=2$

5. 5

   Interpret and check the answer. A slope of $2$ means the line rises $2$ units for every $1$ unit to the right. Checking against the points: going from $(2,-4)$ to $(6,4)$ the run is $4$ and the rise is $8$, and $8=2\times 4$. Reversing the labels gives $\dfrac{-4-4}{2-6}=\dfrac{-8}{-4}=2$, the same value, as it must be.