Interpreting Linear Models in Context
Practice explaining what slope, intercepts, and function values mean in PSAT word problems.
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Questions Covered in This Set
11 cards to master
In y = mx + b, what does b mean in context?
The starting/initial value — what y equals when x = 0 (flat fee, initial amount).
In y = mx + b, what does m mean in context?
The rate of change — how much y changes for each additional one unit of x (the 'per' amount).
In C = 35 + 12h (cost in dollars, h hours), what does 35 represent?
A fixed fee of $35 charged even for 0 hours of work (service/show-up charge).
In C = 35 + 12h, what does 12 represent?
The cost increases $12 for each additional hour of work — $12 per hour.
How do units help you answer interpretation questions fast?
Slope's units are (y-units per x-units), e.g. dollars per hour — which usually eliminates three answer choices.
G = 400 − 8m (gallons, minutes): interpret 400 and −8.
The tank started with 400 gallons; it drains at 8 gallons per minute.
What does the x-intercept mean in a decreasing context model?
The time (input value) when the quantity reaches zero / runs out. Set y = 0 and solve.
Write a model: $50 sign-up fee plus $29 per month for n months.
T = 29n + 50 (50 is one-time, 29 is per-unit).
Taxi: $11 for 3 miles, $17 for 6 miles. Find the model.
m = (17−11)/(6−3) = 2 dollars per mile; 11 = 2(3) + b so b = 5. F = 2d + 5.
What does f(10) = 85 mean in context?
When the input is 10, the predicted output is 85 — stated in the problem's units (not a slope statement).
What is extrapolation trouble on the PSAT?
Using a model far outside its data range, so the prediction may be unreliable.
