Modeling real situations with linear functions — constant rates of change, initial values, and evaluating or interpreting f(x) in context.
46
Total questions
26
Easy
10
Medium
10
Hard
Linear function questions wrap the same slope-and-intercept machinery in function notation and real contexts: water filling a tank, a phone plan's monthly cost, the value of equipment depreciating. You're asked to build the function from a description, evaluate it, or interpret what a specific part means.
Anchor on the pattern f(x) = (rate)(x) + (starting value). When building a model from a word problem, identify the per-unit rate and the initial amount before touching the answer choices — then match. When interpreting, translate the number back into the units of the story: a slope of 6 in a gallons-per-minute context means 6 gallons each minute, full stop.
Straight from the Grind1600 question bank — try each one before revealing the answer.
Correct answer: D
Choice D is correct. It's given that the tank starts with 50 gallons of water. This initial amount can be represented by the constant 50. Each minute, 6 gallons are added, which can be represented by 6m. Thus, the equation w = 6m + 50 gives the amount of water in the tank m minutes after the water began being added.
Choice B is incorrect and may result from switching the rate with the initial amount.
Choice C is incorrect and may result from adding the rate and initial amount.
Choice A is incorrect and may result from conceptual errors.
Correct answer: D
Choice D is correct. Since 85 is a constant, it represents an actual bill amount. To determine what bill it represents, find m such that B(m) = 85: 85 = 85 - 6.50(m - 4). Subtracting 85 from both sides gives 0 = -6.50(m - 4). Dividing both sides by -6.50 yields 0 = m - 4, or m = 4. Since m represents months after January, m = 4 corresponds to May (January + 4 months). Therefore, the average bill is $85 in May.
Choice A is incorrect. Since 85 is a constant, not a multiple of m, it cannot represent a rate of change.
Choice B is incorrect. The difference would require calculating B(5) - B(0).
Choice C is incorrect. The average bill in January is B(0) = 85 - 6.50(0 - 4) = 85 + 26 = 111.
Linear Equations in One Variable
Solving equations of the form ax + b = c, including equations with variables on both sides, fractions, and no-solution or infinite-solution cases.
Linear Equations in Two Variables
Working with equations like y = mx + b: interpreting slope and intercepts, converting between forms, and connecting equations to their graphs.
Linear Inequalities
Solving and interpreting inequalities in one or two variables, including flipping the inequality sign and identifying solution regions.
Systems of Linear Equations
Solving pairs of linear equations by substitution or elimination, and reasoning about when systems have one, none, or infinitely many solutions.
46 Linear Functions questions with step-by-step explanations, woven into a day-by-day study plan built for your test date.
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