Equation of a Line — SAT Math Explained
An algebraic expression representing all points (x, y) that lie on a specific line. Lines can be expressed in multiple equivalent forms, each highlighting different information.
The Core Idea
Every line has an equation; every equation of degree 1 in x and y represents a line. Different forms are more or less convenient depending on what information you're given and what you need to find.
Forms
y = mx + b — slope m and y-intercept b are immediately visible
Ax + By = C — A, B, C are integers, A is positive; useful in systems of equations
y - y₁ = m(x - x₁) — best when you have a point and slope
y = constant — slope = 0
x = constant — undefined slope
Writing Equations Given Information
Use y = mx + b directly
Use point-slope form, then convert if needed
Calculate slope first using m = (y₂-y₁)/(x₂-x₁), then use point-slope
Same slope as original, different y-intercept
Negative reciprocal slope (if original slope is m, perpendicular slope is -1/m)
Parallel And Perpendicular
Same slope, different y-intercepts — lines never intersect
Slopes are negative reciprocals — their product = -1
Common Errors to Avoid
Flipping numerator and denominator when finding negative reciprocal for perpendicular slopes
Using the slope formula backwards (x-change in numerator)
Not converting to the required form when the problem specifies one
Practice: Equation of a Line
5 SAT-style questions. Select your answer and get an instant explanation.
Slope through (0,0) and (2,4)?
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