Math · Algebra · H.B.
Linear functions
Linear functions are slope, intercept, and rate-of-change in context. Top-band misses here are almost never 'I don't know slope.' They are 'I read the wrong quantity off the table.'
What Bluebook is testing
H.B. is f(x) = mx + b and everything that means in words: rate, starting value, when two plans cost the same, what the intercept actually is.
How it shows up
Tables, graphs, and worded rates. Hard items give two representations and ask you to translate — slope from a table that is not consecutive integer x-values, or the intercept of a model that never hits x = 0 in the story.
A method that survives Module 2
Name m and b in the story before you compute: 'm is dollars per month, b is the signup fee.' For a table, pick two clean points and compute slope; then plug one point for b. If two plans are compared, set the functions equal — do not subtract the intercepts and stop.
Traps that look like knowledge
- Using Δy/Δx on rows that are not one unit apart and forgetting to divide
- Mixing slope (rate) with the intercept (starting value)
- Answering f(a) when they asked for a, or the reverse
- Reading a graph intercept from a cropped axis that does not start at zero
Questions
- What is "Linear functions" on the Digital SAT?
- It is an official College Board skill in Digital SAT Math. The wording on Bluebook matches the domain taxonomy Drilled uses in drills, analytics, and the notebook.
- How does Drilled train Linear functions?
- Filter the bank to the skill, run a timed drill, autopsy every miss, and let the notebook bring the same pattern back. Domain drills and full section sims include the skill at the official mix.
- What is the most common trap on Linear functions?
- Using Δy/Δx on rows that are not one unit apart and forgetting to divide
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