SAT linear models: what the slope and intercept mean in the story
You can find the slope. The question is not asking you to. It is asking what the slope means, in litres and hours — and the wrong choices are all real numbers lifted from the same equation.
Why it happens
Interpretation questions strip out the computation and test only the mapping between symbol and situation. Because both numbers in the model appear in the choices, an answer that swaps them looks exactly as plausible as the right one, and there is no arithmetic to catch the swap.
See the trap
V(t) = −8t + 96 gives the litres of paint left after t hours of spraying. What does 96 represent?
"96 litres are used each hour" — the right number attached to the wrong role.
The paint in the tank before spraying started. 96 is the value at t = 0; −8 is the litres-per-hour rate.
How to actually fix it
- 1Set the variable to zero. Whatever the model gives you is what the intercept means — which is the starting amount only when zero is where the situation starts, so check what the variable counts.
- 2Increase the variable by exactly one. The change is what the slope means — and it always carries the words "per" one unit.
- 3Read the sign: a negative slope means the output falls as the input rises. Whether that is "used up" depends on what the output measures — here, paint left in a tank.
Practice this trap · 10 real questions
Each of these is a question from the free bank that turns on the mistake above — the trap is the reason its wrong answer looks right. Easiest first.
Showing 8 of 10. Keep going in Algebra →
FAQ
Does this work when the model is not linear?
The x = 0 test still gives the starting value, but the "per one unit" test does not — in an exponential model the change is a multiplier, not a fixed amount. That difference is itself a favorite SAT question.
How do I stop repeating this mistake?
Reading the explanation isn't enough — your brain needs to beat the trap on a fresh question. Practice the skill in the kaoshen.co question bank: miss one and it is logged with the exact error, then brought back to you three days later and again after fourteen.
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