Are these Linear Equations notes free?

Yes. The full 3-page Linear Equations sheet is free inside CapCompass, which runs in your browser with no account needed.

What does the Linear Equations revision sheet cover?

The four forms worth recognising, one variable, standard, two variables, standard, slope-intercept, point-slope, through (x_1,y_1), Slope, three ways to get it, from two points, rise over run, from Ax + By = C, Two lines that never cross, and one that never tilts, Slope relationships to know cold, Parallel.

Is this for Digital SAT SAT Math?

Yes, it is written for the Digital SAT SAT Math syllabus.

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Linear Equations — Digital SAT SAT Math revision notes

A 3-page visual revision sheet for Linear Equations, written for Digital SAT SAT Math. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

Linear Equations revision notes, page 1 of 3 — A preview of page 1 — all 3 pages open full size in the app.

Linear Equations in one look

one unknown or two: isolate, rearrange, and always substitute back

The four forms worth recognising

one variable, standard ax + b = 0
two variables, standard Ax + By = C
slope-intercept y = mx + b
point-slope, through (x_1,y_1) y - y_1 = m(x - x_1)

Q. Solve 4(x - 3) + 5x = 2x + 9.

distribute the 4 across the bracket: 4x - 12 + 5x = 2x + 9
collect like terms on the left: 9x - 12 = 2x + 9
move the x terms one way, the numbers the other: 9x - 2x = 9 + 12
7x = 21, so divide both sides by 7

Answer: x = 3

Slope, three ways to get it

from two points m = y_2 - y_1/x_2 - x_1
rise over run m = Δ y/Δ x
from Ax + By = C m = -A/B,quad b = C/B

how many solutions does ax + b = cx + d have

a is not equal to c — exactly one solution: the x terms do not cancel, so x lands on one number
a = c but b is not equal to d — no solution: x cancels and leaves a false number statement
a = c and b = d — infinitely many solutions: the two sides are literally the same expression

Page 1 of 3. The full sheet, all 3 pages, opens free in the app.

What this Linear Equations sheet covers

The four forms worth recognising
one variable, standard
two variables, standard
slope-intercept
point-slope, through (x_1,y_1)
Slope, three ways to get it
from two points
rise over run
from Ax + By = C
Two lines that never cross, and one that never tilts
Slope relationships to know cold
Parallel
Perpendicular
Same line
Shifted up by k
Reading a linear model in words
Traps that cost points
Tricks that save time

Open the full Linear Equations sheet →Free, works offline, no account needed. All 3 pages, plus a study plan built around your own exam dates.

How CapCompass uses this sheet

These notes are not a standalone PDF. CapCompass plans SAT Math chapter by chapter against your real exam dates and free hours, and when the plan reaches Linear Equations the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.