Working with equations like y = mx + b: interpreting slope and intercepts, converting between forms, and connecting equations to their graphs.
49
Total questions
22
Easy
13
Medium
14
Hard
These questions test whether you can move fluently between a linear equation and its meaning: slope as a rate of change, y-intercept as a starting value, and x-intercept as where the output hits zero. You'll convert between standard form and slope-intercept form, match equations to graphs, and find equations from two points.
Get ruthless about converting to y = mx + b — almost every question becomes easier in that form. When a question gives a real-world context, translate immediately: slope is always "change in y per one unit of x," and the intercept is the value when x = 0. The built-in Desmos calculator can graph any form instantly, which turns many of these into visual checks.
Straight from the Grind1600 question bank — try each one before revealing the answer.
Correct answer: C
Choice C is correct. The expression 2x + 3y is exactly half of the left-hand side of the given equation, since 4x + 6y = 2(2x + 3y). Dividing both sides of the equation 4x + 6y = 36 by 2 yields 2x + 3y = 18. This value is the same for every ordered pair (x, y) that satisfies the given equation. Choice A is incorrect and may result from dividing 36 by 4, the coefficient of x. Choice B is incorrect and may result from dividing 36 by 3, the coefficient of y in the requested expression. Choice D is incorrect and may result from multiplying 36 by 2 instead of dividing by 2.
Correct answer: A
Choice A is correct. An equation defining a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept. The slope m = (16 - 4)/(5 - 1) = 12/4 = 3. Substituting m = 3 and the point (1, 4) into y = mx + b gives 4 = 3(1) + b, or 4 = 3 + b. Subtracting 3 from both sides yields b = 1. Therefore, the equation is y = 3x + 1.
Choice B is incorrect and may result from using 4 as the y-intercept without calculation.
Choice C is incorrect. This line passes through the origin, not (1, 4).
Choice D is incorrect and may result from using 4 as the slope.
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 Functions
Modeling real situations with linear functions — constant rates of change, initial values, and evaluating or interpreting f(x) in context.
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.
49 Linear Equations in Two Variables questions with step-by-step explanations, woven into a day-by-day study plan built for your test date.
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