Back

Equations of Lines: Forms, Intercepts, and Parameters

SAT MathAlgebraFoundation

Move fluently among slope-intercept, point-slope, and standard forms.

What you need to know

  • Slope-intercept form y = mx + b shows slope and y-intercept directly.
  • Point-slope form y − y₁ = m(x − x₁) is fastest from a point and slope.
  • In Ax + By = C, intercepts come from setting the other variable to zero.
  • Parallel lines share slope; nonvertical perpendicular slopes multiply to −1.

The AYLOTI method

  1. Identify the information provided.
  2. Choose the form that uses it directly.
  3. Substitute carefully.
  4. Convert form only if the question requires it.

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

Worked example

Find the line through (3, −2) with slope 4.

  1. Use point-slope: y + 2 = 4(x − 3).
  2. Expand: y + 2 = 4x − 12.
  3. Subtract 2: y = 4x − 14.

Answer: y = 4x − 14.

Common SAT traps

  • Using the point’s x-coordinate as the y-intercept.
  • Forgetting the sign in y − (−2).
  • Calling equal intercepts equal slopes.
Quick check

What is the slope of 3x + 2y = 8?

−3/2.

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.
author avatar