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Slope: Calculate and Interpret Rate of Change

SAT MathAlgebraFoundation

Connect slope across points, tables, graphs, equations, and contexts.

What you need to know

  • Slope m = change in y ÷ change in x.
  • Use the same point order in numerator and denominator.
  • In context, slope carries output units per input unit.
  • Positive, negative, zero, and undefined slopes describe different line directions.

The AYLOTI method

  1. Choose two reliable points.
  2. Compute Δy and Δx in matching order.
  3. Simplify the ratio.
  4. Interpret the sign and units.

AYLOTI • Sir Hunain Zia • SAT Score 1594/1600 • 154 Total A Grades (Personal), 11 World Records, 7 Distinctions

Worked example

A tank contains 120 L at t = 0 and 90 L at t = 5 minutes. Find and interpret slope.

  1. Δvolume = 90 − 120 = −30 L.
  2. Δtime = 5 − 0 = 5 min.
  3. Slope = −30/5 = −6 L/min.

Answer: The volume decreases by 6 liters per minute.

Common SAT traps

  • Reversing only one subtraction.
  • Reporting a rate without units.
  • Confusing y-intercept with slope.
Quick check

Find the slope through (2, 5) and (6, 13).

2.

Before you move on

  • Explain the core rule without looking back.
  • Redo the worked example using your own steps.
  • Write the trap you are most likely to fall for.
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