Algebra • 35% of test
Linear Functions
Select your difficulty level to start practicing. We recommend mastering each level before moving to the next.
Beginner5 Sets
Beginner Practice
Start here to build your foundation. Clear problems and straightforward calculations.
Target Score
400-550
Intermediate5 Sets
Intermediate Practice
Level up with more complex equations and multi-step problems.
Target Score
550-700
Advanced3 Sets
Advanced Practice
Master the hardest concepts. Complex word problems and abstract applications.
Target Score
700-800
What is Linear Functions?
Linear functions describe relationships with constant rates of change. The SAT tests slope, intercepts, parallel/perpendicular lines, and interpreting linear models in context.
Step-by-Step Strategy
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Frequently Asked Questions
What is slope?
Slope measures steepness and direction. It's the ratio of vertical change to horizontal change (rise over run).
What makes lines parallel?
Lines with the same slope are parallel. They never intersect (unless they're the same line).
What makes lines perpendicular?
Perpendicular lines have slopes that are negative reciprocals. If one slope is 2, the perpendicular slope is -1/2.
What does y-intercept represent in context?
Often the starting value, initial amount, or fixed cost. Understanding intercepts is critical for <a href='/math'>high-scoring SAT Math performance</a>.
How do I find slope from a graph?
Pick two clear points and calculate rise/run. Count grid squares for accuracy.
What's point-slope form?
y - y₁ = m(x - x₁). Useful when you know a point and slope but not the y-intercept.
What is the 'Standard Form' of a linear function?
Ax + By = C. This form is often useful for finding intercepts quickly by setting x or y to zero.
How do I find the x-intercept of a function f(x)?
Set f(x) = 0 and solve for x. Refine your function analysis skills with our <a href='/math/linear-functions/intermediate'>Intermediate Linear Functions practice</a>.
What does a 'zero slope' line look like?
It is a horizontal line (y = b). The rate of change is zero, meaning the output never changes regardless of the input.
What is an 'undefined slope'?
A vertical line (x = a). The rate of change is infinite because there is no horizontal change ('run' is zero).
How do I find the equation of a line passing through two points?
1) Find slope (m) using the formula, 2) Use one point and m in point-slope form or y = mx + b to find b.
What is the relationship between the slopes of perpendicular lines?
Their product is always -1 (unless one is vertical). This is why they are called negative reciprocals.
How can I tell if a table represents a linear function?
Check if the rate of change (change in y / change in x) is constant between every pair of points in the table.
What is a 'linear model' in a word problem?
It's an equation that represents a real-world scenario with a starting value (y-intercept) and a constant rate (slope).
Does f(x) always mean y?
In the context of the SAT coordinate plane, yes. f(x) represents the vertical coordinate for a given horizontal input x.