SAT Linear Functions Questions
Reading and writing f(x) = mx + b. Slope as a rate, the intercept as a starting value, and turning a word problem into both.
In short
- Linear Functions is part of Algebra, about 35% of the scored Math questions: 13 to 15 on every test.
- Math questions from all four areas are mixed in each module and arranged from easiest to hardest.
- Slope sign is the trap Rivie's practice tests set most often in Linear Functions questions.
Common traps
Most common first, from Rivie's ten practice tests.
Slope sign
Compute slope from two points or a graph; the wrong choice gets the magnitude correct but the sign reversed (negative read as positive or vice versa).
The usual mistake: You compute Δy / Δx but assign the sign by 'it goes up' instead of by the actual difference. Lines descending left-to-right are the most common trap.
Perpendicular slope
Perpendicular lines have slopes whose product is −1 (negative reciprocals). The wrong choice flips the sign without flipping the fraction (or vice versa).
The usual mistake: You take the slope, change the sign, and call it perpendicular, forgetting to also invert the numerator and denominator.
Rate vs. initial value
Word problems modeling 'starts at X, increases by Y per period' have X as the initial value and Y as the rate. The wrong choice picks the wrong one for the question being asked.
The usual mistake: You read 'increases by' and grab the number after it without distinguishing whether the question wants the starting amount or the rate of change.
Linear model from two points
Given two (x, y) pairs that fit a linear model: find slope = Δy/Δx, then back-solve for the y-intercept by plugging one point into y = mx + b.
The usual mistake: You compute slope correctly and then plug into y = mx + b without solving for b, picking whichever intercept choice has the right sign by feel.
Try a question
From Rivie's practice tests. Pick an answer to see why it is right or wrong.
A line in the xy-plane passes through the points (2, 5) and (4, 11). What is the slope of the line?
Video lessons
Free on YouTube, picked for this topic.