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Lines and Linear Functions flashcards
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- Recover a missing coordinateCoordinate Plane, Slope, and Rate of Change
- The rise must equal slope times run.
- When should I use slope from two points?Coordinate Plane, Slope, and Rate of Change
- Compute slope with consistent coordinate order.
- What method supports recover a missing coordinate?Coordinate Plane, Slope, and Rate of Change
- y₂ = y₁ + m(x₂ − x₁)
- Rate in contextCoordinate Plane, Slope, and Rate of Change
- Read slope as how much output changes for one input step.
- Slope from two pointsCoordinate Plane, Slope, and Rate of Change
- Rise divided by run tells how steep the line is.
- What must I check in coordinate plane, slope, and rate of change?Coordinate Plane, Slope, and Rate of Change
- Slope is undefined for a vertical line; use change in y divided by change in x
- What method supports rate in context?Coordinate Plane, Slope, and Rate of Change
- rate = output change/input change
- What method supports slope from two points?Coordinate Plane, Slope, and Rate of Change
- m = (y₂ − y₁)/(x₂ − x₁), x₂ ≠ x₁
- When should I use recover a missing coordinate?Coordinate Plane, Slope, and Rate of Change
- Use a known slope to constrain an unknown point.
- When should I use rate in context?Coordinate Plane, Slope, and Rate of Change
- Interpret slope with units.
- Standard form conversionsSlope-Intercept, Point-Slope, and Standard Forms
- Solve for y before reading its slope.
- When should I use slope-intercept form?Slope-Intercept, Point-Slope, and Standard Forms
- Read a slope and intercept from y = mx + b.
- What method supports standard form conversions?Slope-Intercept, Point-Slope, and Standard Forms
- Ax + By = C ⇒ m = −A/B, B ≠ 0
- Point-slope formSlope-Intercept, Point-Slope, and Standard Forms
- Start from a known point and add slope times the input change.
- Slope-intercept formSlope-Intercept, Point-Slope, and Standard Forms
- The multiplier of x is the slope; the separate constant is the y-intercept.
- What must I check in slope-intercept, point-slope, and standard forms?Slope-Intercept, Point-Slope, and Standard Forms
- Vertical lines use x = constant and do not have finite slope
- What method supports point-slope form?Slope-Intercept, Point-Slope, and Standard Forms
- y − y₁ = m(x − x₁)
- What method supports slope-intercept form?Slope-Intercept, Point-Slope, and Standard Forms
- y = mx + b
- When should I use standard form conversions?Slope-Intercept, Point-Slope, and Standard Forms
- Find slope by isolating y in a standard-form equation.
- When should I use point-slope form?Slope-Intercept, Point-Slope, and Standard Forms
- Use a point and slope to predict another value.
- Graph information without a pictureFinding Equations from Points, Tables, and Graphs
- Turn each intercept into a full coordinate pair.
- When should I use line through two points?Finding Equations from Points, Tables, and Graphs
- Determine an intercept after calculating slope.
- What method supports graph information without a picture?Finding Equations from Points, Tables, and Graphs
- intercepts (a,0) and (0,b) give m = −b/a, a ≠ 0
- Linear tablesFinding Equations from Points, Tables, and Graphs
- Compare rates, not just raw differences.
- Line through two pointsFinding Equations from Points, Tables, and Graphs
- Find the rate, then find where the line starts.
- What must I check in finding equations from points, tables, and graphs?Finding Equations from Points, Tables, and Graphs
- Use the same x and y meanings across a table, equation, and graph
- What method supports linear tables?Finding Equations from Points, Tables, and Graphs
- (Δy)/(Δx) = constant for a linear table
- What method supports line through two points?Finding Equations from Points, Tables, and Graphs
- b = y₁ − mx₁
- When should I use graph information without a picture?Finding Equations from Points, Tables, and Graphs
- Recover a line from its intercepts.
- When should I use linear tables?Finding Equations from Points, Tables, and Graphs
- Infer a constant rate from equal or unequal input intervals.
- Both intercepts in a modelIntercepts and Their Meaning in Context
- Each intercept uses the entire resource on one choice.
- When should I use starting value?Intercepts and Their Meaning in Context
- Interpret a y-intercept in context.
- What method supports both intercepts in a model?Intercepts and Their Meaning in Context
- ax + by = C ⇒ x-intercept C/a and y-intercept C/b
- Zero outputIntercepts and Their Meaning in Context
- Ask when the output reaches zero.
- Starting valueIntercepts and Their Meaning in Context
- Read the output at input zero.
- What must I check in intercepts and their meaning in context?Intercepts and Their Meaning in Context
- The x-intercept is (a,0), while the y-intercept is (0,b); consider feasible input values
- What method supports zero output?Intercepts and Their Meaning in Context
- mx + b = 0 ⇒ x = −b/m, m ≠ 0
- What method supports starting value?Intercepts and Their Meaning in Context
- y-intercept = f(0)
- When should I use both intercepts in a model?Intercepts and Their Meaning in Context
- Relate a total constraint to its axis intercepts.
- When should I use zero output?Intercepts and Their Meaning in Context
- Find an x-intercept and attach its meaning.
- Perpendicular line through a pointParallel and Perpendicular Lines
- Direction gives the slope; the point locates the line.
- When should I use parallel slopes?Parallel and Perpendicular Lines
- Find the slope of a line parallel to a given line.
- What method supports perpendicular line through a point?Parallel and Perpendicular Lines
- b = y₀ − mx₀
- Perpendicular slopesParallel and Perpendicular Lines
- Flip the fraction and change the sign.
- Parallel slopesParallel and Perpendicular Lines
- Parallel lines share a slope.
- What must I check in parallel and perpendicular lines?Parallel and Perpendicular Lines
- Parallel distinct nonvertical lines have equal slopes; horizontal and vertical lines form a special perpendicular pair
- What method supports perpendicular slopes?Parallel and Perpendicular Lines
- m₂ = −1/m₁, m₁ ≠ 0
- What method supports parallel slopes?Parallel and Perpendicular Lines
- m₁ = m₂ for parallel nonvertical lines
- When should I use perpendicular line through a point?Parallel and Perpendicular Lines
- Combine a direction condition with a known point.
- When should I use perpendicular slopes?Parallel and Perpendicular Lines
- Use a negative reciprocal to find a perpendicular direction.
- Build a linear modelLinear Function Notation and Modeling
- Use one observation to anchor the constant-rate rule.
- When should I use evaluate a linear function?Linear Function Notation and Modeling
- Use function notation as input substitution.
- What method supports build a linear model?Linear Function Notation and Modeling
- f(t) = f(t₀) + m(t − t₀)
- Interpret a coefficientLinear Function Notation and Modeling
- The slope times the input change gives the output change.
- Evaluate a linear functionLinear Function Notation and Modeling
- Put the input into the rule and calculate the output.
- What must I check in linear function notation and modeling?Linear Function Notation and Modeling
- A contextual domain may restrict a linear function to nonnegative or integer inputs
- What method supports interpret a coefficient?Linear Function Notation and Modeling
- f(x + h) − f(x) = mh
- What method supports evaluate a linear function?Linear Function Notation and Modeling
- f(a) = ma + b when f(x) = mx + b
- When should I use build a linear model?Linear Function Notation and Modeling
- Determine a model from a rate and one observed value.
- When should I use interpret a coefficient?Linear Function Notation and Modeling
- Connect a linear rate to output changes over an interval.