Linear Equations — The Foundation
The single most tested math topic on the SAT.
Slope-intercept form: y = mx + b
m = slope (rise/run), b = y-intercept
Standard form: Ax + By = C
Slope = -A/B, y-intercept = C/B
Point-slope form: y - y1 = m(x - x1)
Use when you have a point and slope.
Key skills:
1. Convert between all three forms
2. Find slope between two points: m = (y2 - y1) / (x2 - x1)
3. Parallel lines have same slope
4. Perpendicular lines have negative reciprocal slopes
5. Interpret slope and intercept in context (rate of change, starting value)
SAT favorite: "What does the number 15 represent in the equation y = 3x + 15?" Answer: the starting value / y-intercept / initial amount.
Reference:
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