SAT Math: Calculate slope from two points
32+ practice questions in Praczo
The concept, explained
- 1
Slope formula: m = (y2 - y1) / (x2 - x1). It measures vertical change per unit horizontal change.
- 2
Pick one point as (x1, y1) and the other as (x2, y2), then stick with that choice in both numerator and denominator. Swapping order mid-calculation flips the sign.
- 3
Horizontal lines have slope 0 (y2 = y1). Vertical lines have undefined slope (x2 = x1, division by zero).
- 4
A positive slope rises left-to-right; a negative slope falls. Larger absolute value = steeper line.
- 5
Be careful with negative coordinates: (−2 − 5) = −7, not 7 — a sign error here flips the slope.
- ✗ Using the wrong order ("(x2 - x1) / (y2 - y1)") — that gives run/rise, which is the reciprocal of slope.
- ✗ Inconsistent ordering — subtracting y2 - y1 but then x1 - x2, which flips the sign.
- ✗ Calling a vertical line’s slope 0 instead of undefined.
SAT-style practice
What is the slope of the line passing through (-2, 7) and (4, -5)?
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