Darasa la 6–8AlgebraImepangwa
Linear relationships and simultaneous equations
Lines in the coordinate plane: slope as a constant rate of change, the form y = mx + b, linear functions, and solving pairs of simultaneous linear equations graphically and algebraically.
math.algebra.linear-relationships
Somo la mada hii bado halijaandikwa. Muhtasari ulio hapa chini ni sehemu ya ramani ya mtaala na haujakaguliwa.
Inajengwa juu ya
Linear equations and inequalitiesFunctionsThe coordinate planeRatios, rates and proportional reasoning
Masharti ya awali ya lazima 14 (hadi chini kabisa)
Utajifunza
- Compute the slope of a line from two points and interpret it as a rate of change.
- Write the equation of a line from its slope and a point, and recognise linear functions in tables, graphs and formulas.
- Solve two simultaneous linear equations by substitution, elimination and graphing, and interpret the cases with no solution or infinitely many.
Fasili
- The slope of the line through (x₁, y₁) and (x₂, y₂), with x₁ ≠ x₂, is (y₂ − y₁)/(x₂ − x₁).
- A linear function has the form f(x) = mx + b.
- A solution of a system of equations satisfies every equation in the system at once.
Nadharia
- The slope between any two points on a non-vertical line is the same.
- Two distinct lines in the plane meet in exactly one point unless they are parallel, that is, have equal slopes or are both vertical.
- A system of two linear equations in two unknowns has exactly one solution, no solution, or infinitely many solutions.
Mawazo potofu ya kawaida
- Computing slope as 'run over rise'.
- Believing every straight-line relationship is proportional.
- Giving a vertical line slope zero; its slope is undefined.
Inaelekea kwa
Ugunduzi wa hiari
- Function machines in sequence Composing two linear functions gives another: applying x ↦ m₂x + b₂ and then x ↦ m₁x + b₁ gives x ↦ m₁m₂x + (m₁b₂ + b₁).
Njia za kujifunza
Usomaji zaidi
- I. M. Gelfand and A. Shen, Algebra (1993)