How are Linear Functions and Inequalities tested on the SAT?

Questions ask you to find slope and intercepts, write a line's equation, solve or graph inequalities, and interpret slope and intercept as a rate and starting value in real-world contexts.

What's the single most important rule for inequalities?

Reverse the inequality sign whenever you multiply or divide both sides by a negative number. Forgetting this flips the solution to the wrong direction and is the most common error on these questions.

What's the fastest way to improve at Linear Functions and Inequalities?

Use slope as rise over run consistently, and in word problems read slope as 'per' and intercept as the value when x is zero. Test any inequality solution by plugging in a sample value.

SAT Math · Algebra

Linear Functions and Inequalities

This skill covers linear functions and inequalities: reading slope and intercepts, writing the equation of a line, and solving or graphing inequalities. Much of it comes down to understanding what slope and intercept mean, both algebraically and in real-world context. The single most important rule is flipping the inequality sign when you multiply or divide by a negative.

Quick answer

Linear Functions and Inequalities is a digital SAT Math skill covering slope and intercepts, writing and graphing lines, and solving linear inequalities — including the rule that the inequality sign flips when you multiply or divide by a negative.

What it tests

Finding slope and intercepts from an equation, graph, or two points
Writing the equation of a line in slope-intercept or standard form
Solving linear inequalities and representing the solution set
Interpreting slope and intercept as a rate and a starting value in context
Graphing an inequality and identifying which region satisfies it

Common mistakes

Forgetting to reverse the inequality sign when multiplying or dividing by a negative number
Swapping the rise and run when computing slope from two points
Confusing the y-intercept (starting value) with the slope (rate of change) in a context problem
Shading the wrong side when graphing an inequality

How to improve

Memorize slope as rise over run, or (y2 − y1) / (x2 − x1), and use it consistently
In word problems, translate slope as 'per' and intercept as the value when x is zero
Flag every negative multiplication or division in an inequality to remember the sign flip
Test an inequality's solution by plugging in a sample value
Sketch quick graphs to confirm which region or direction is correct

Worked example

Solve for x: -3x + 5 < 14.

Subtract 5 from both sides: -3x < 9. Now divide by -3 and flip the inequality sign: x > -3. Forgetting to flip the sign here is the classic error and gives the wrong direction.

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Related SAT Math skills

AlgebraLinear Equations and Systems Advanced MathEquivalent Expressions Advanced MathQuadratics and Nonlinear Functions Problem-Solving and Data AnalysisRatios, Rates, and Proportions

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Frequently asked questions

How are Linear Functions and Inequalities tested on the SAT?: Questions ask you to find slope and intercepts, write a line's equation, solve or graph inequalities, and interpret slope and intercept as a rate and starting value in real-world contexts.
What's the single most important rule for inequalities?: Reverse the inequality sign whenever you multiply or divide both sides by a negative number. Forgetting this flips the solution to the wrong direction and is the most common error on these questions.
What's the fastest way to improve at Linear Functions and Inequalities?: Use slope as rise over run consistently, and in word problems read slope as 'per' and intercept as the value when x is zero. Test any inequality solution by plugging in a sample value.