Flashcard: Mastering Coordinate Geometry and Linear Equations — 16 carte

Line equation — through two points?

Use slope and point-slope form to derive it.

Slope formula — calculation?

(y₂ - y₁) / (x₂ - x₁)

Point-slope form — purpose?

Expresses a line using a point and slope.

Standard form — of a line?

Ax + By = C, with constants A, B, C.

Distance formula — between points?

√[(x₂ - x₁)² + (y₂ - y₁)²]

Midpoint formula — finds?

The middle point between two coordinates.

Substitution method — solves?

Systems by isolating and substituting variables.

Elimination method — mechanism?

Adding or subtracting equations to cancel a variable.

Word problems — translate into?

Algebraic equations representing the scenario.

Linear systems — solutions?

Values satisfying all equations simultaneously.

Price-quantity — relationship?

Demand varies with price, modeled by equations.

Rounding answers — in problems?

Adjust to nearest whole or practical number.

Solve for variables — how?

Manipulate equations to isolate unknowns.

Verify solutions — by?

Substituting back into original equations.

Coordinate distance — formula?

√[(x₂ - x₁)² + (y₂ - y₁)²]

Midpoint calculation — formula?

( (x₁ + x₂)/2, (y₁ + y₂)/2 )