The lines y = -4x + 17 and y = -x - 1 intersect at point P. What is the y-coordinate of P?
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The Desmos Way
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Given on the test
Printed at the start of every SAT math section. Look these up on the day — the week you would spend memorising them belongs to everything below.
Area and perimeter
Right triangles only. c is the hypotenuse.
Special right triangles
The short leg faces the 30°.
The two legs are equal.
Volume
Facts
Algebra
Lines
Rise over run. A negative slope falls left to right.
b is the value when x = 0.
The fast form when you are handed one point and a slope.
Slope -A/B, y-intercept C/B, x-intercept C/A.
Same m, different b — they never meet.
Flip the fraction and change the sign.
Reading a linear model
Two linear equations
Different slopes, so the lines cross exactly once.
Same slope, different intercept — parallel.
The same line written twice.
Absolute value and inequalities
Only when k ≥ 0. A negative right-hand side has no solution.
One band between two numbers.
Two pieces going opposite ways.
How far x is from a. "Within 3 of 10" is |x - 10| ≤ 3.
Advanced Math
The three forms of a quadratic
c is the y-intercept, free of charge.
The vertex is (h, k). Note the minus sign inside.
r₁ and r₂ are the x-intercepts.
Then substitute that x back in for the y.
The same line the vertex sits on.
Solving a quadratic
Positive: two solutions. Zero: one, and the curve touches the axis. Negative: none.
Factoring patterns
Two numbers that multiply to the last and add to the middle.
Exponents and radicals
A negative exponent means reciprocal, never a negative answer.
xa/b is the b-th root of xa.
Growth and decay
a is where it starts, b is what it multiplies by each step.
"Up 8% a year" is a multiplier of 1.08.
Halves every 5 — the period goes under the t.
Functions
The sign inside does the opposite of what it looks like.
Taller by a factor of a; the x-intercepts stay put.
Work from the inside out.
Polynomials and rational expressions
Problem Solving and Data Analysis
Percent
Divide by where you started, never by where you ended.
Ratio, rate and proportion
Statistics
Probability
Samples, studies and models
A point above the line has a positive residual.
Geometry and Trigonometry
Angles
Triangles
And their multiples — 6-8-10 is the same triangle.
Circles
Center (h, k), radius r — not r2.
Complete the square in x and in y to get back to the center.
When both sit on the same arc.
Trigonometry
The SAT asks this one directly, most years.
The Desmos moves
Most SAT algebra is a picture. These are the moves that turn a question into one, and they are worth more marks than any formula on this sheet.