Linear equations, systems, and function notation concepts tested on the SAT math section, explained conceptually rather than as bare formulas.
40 cards · basic cards · AI-written, checked twice. Edit anything.
- What does slope measure in a linear relationship?
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The rate of change, or how much the y-value changes for every unit change in x.- If a line has slope 3, what does that mean?
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For every 1 unit you move right, the y-value increases by 3 units.- What is the y-intercept of a line?
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The point where the line crosses the y-axis, or the y-value when x equals 0.- What is the x-intercept of a line?
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The point where the line crosses the x-axis, or the x-value when y equals 0.- What is slope-intercept form?
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The form y = mx + b, where m is the slope and b is the y-intercept.- What does point-slope form allow you to do?
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Write the equation of a line using a known point (x1, y1) and the slope m: y - y1 = m(x - x1).- What is standard form of a linear equation?
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Ax + By = C, where A, B, and C are constants (usually integers) and A and B are not both zero.- What is true about the slopes of two parallel lines?
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They have the same slope.- What is the relationship between the slopes of two perpendicular lines?
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Their slopes are negative reciprocals of each other; if one has slope m, the other has slope -1/m.- What does it mean to solve an equation?
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To find the value or values of the variable that make the equation true.- When does a linear equation in one variable have no solution?
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When the equation simplifies to a false statement, like 0 = 5 (parallel lines that never meet in a system context).- When does a linear equation have infinitely many solutions?
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When the equation simplifies to an identity, like 0 = 0 (the same line represented two ways).- What is a system of linear equations?
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Two or more linear equations with the same variables, solved together to find values that satisfy all equations at once.- What does the solution to a system of two equations represent geometrically?
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The point where the two lines intersect (if a unique solution exists).- What is a consistent system of equations?
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A system that has at least one solution (the lines intersect at one point or are the same line).
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