What we see: a slope question. We need how steep the line through \((-1, 4)\) and \((3, -6)\) is, and which way it tilts.
Step 1. Check the direction first.
What we see: going from \(x = -1\) to \(x = 3\) (left to right), y goes from 4 down to \(-6\).
What it means: the line falls as we move right, so the slope is negative.
What we do and why: this alone rules out D and E, which are positive. A quick sign check catches the most common slip before any arithmetic.
Step 2. Find the change in y and the change in x.
What we see: y goes from 4 to \(-6\); x goes from \(-1\) to 3.
What it means: change in y \(= -6 - 4 = -10\). Change in x \(= 3 - (-1) = 4\). Subtracting a negative adds, so it is 4, not 2.
What we do and why: we subtract in the same order on top and bottom (second point minus first point both times), so the sign comes out right.
Step 3. Divide.
What we see: \(-10\) over 4.
What it means: slope \(= \dfrac{-10}{4} = -\dfrac{5}{2}\).
What we do and why: slope is always change in y divided by change in x, never the other way.
The trap: working out \(3 - (-1)\) as 2 gives \(-5\), which is not a choice, and then people guess B. Flipping the fraction gives \(-\frac{2}{5}\), also not a choice, which pushes people to C.
Takeaway: slope is (second y minus first y) over (second x minus first x). Keep the same order on top and bottom, and check the sign by asking whether the line rises or falls left to right.
Answer: A
