Linear equations and substitution
Literal equations and equivalent forms
Straight-line graphs and gradient
Linear inequalities
Equations of straight lines
Linear modelling
Simultaneous equations
Systems with three or four unknowns
Points and lines
Coordinate geometry
Recognise whether an equation is linear from the power on its unknowns Substitute known values into a formula and evaluate it correctly Solve two-step linear equations by inverse operations in reverse order Solve equations with a scaled bracket by expanding or dividing first Solve equations with the unknown inside a fraction by clearing the denominator first Solve equations with unknowns on both sides by collecting them onto one side Translate a described situation into a linear equation in one unknown Turn an equation's exact solution into the answer the situation demands Isolate a nominated subject in a linear literal equation by applying equivalent operations to the whole of both sides and simplifying only valid common factors Recognise equivalent point–gradient, gradient–intercept and primitive general forms of the same line, including horizontal and vertical edge cases Rearrange a linear equation into y = a + bx by inverse operations Build a table of values from a formula by independent substitution Read coordinates off a graphed line respecting its axis scales Classify a graphed line's slope as positive, negative, zero or undefined Compute a slope from a graph as rise over run between two points Compute a slope from two coordinate pairs with the slope formula Solve a one-variable linear inequation, reversing the order relation exactly when multiplication or division by a negative value occurs State whether the boundary is included and identify which side of a one- or two-variable linear boundary satisfies the inequation, using an exact test point where useful Identify the intercept and slope in y = a + bx, including its edge shapes Plot a table of values and draw the straight line through the points Sketch a line from its equation using the intercept and one more point Find a graphed line's equation from its intercept and two well-defined points Find the equation of the line through two points Write a linear model from a description with signed intercept and rate State and respect a linear model's domain of interpretation Use a linear model to predict a response or solve for an explanatory value State in context words what a model's intercept and slope mean Distinguish a direct-proportion rule from a general linear rule, determine the exact constant of proportionality, and recognise that the graph contains the origin Read the point of intersection of two graphed lines Check a claimed solution or point by substituting into the original equation Solve a pair of simultaneous linear equations for the shared (x, y) Recognise from equal slopes that a system has no solution or every point Translate a two-condition description into a pair of equations in two unknowns Solve a practical simultaneous pair and answer the question asked Solve a non-singular system of three or four linear equations by exact elimination or substitution, preserving variable order and checking every original equation Determine exactly whether a point lies on, above or below a non-vertical line, or to the left or right of a vertical line Verify whether three or more points are collinear by equal gradients sharing a common point or by exact substitution into one line equation Find the exact intersection of two lines and verify whether it lies on every remaining line Determine a parameter value that makes a point incident, lines parallel or perpendicular, a system non-unique, or several lines concurrent Use equal gradients for parallel oblique lines and product negative one for perpendicular oblique lines, with explicit horizontal–vertical edge cases Convert between the gradient of a non-vertical line and its angle measured anticlockwise from the positive horizontal direction, returning an obtuse angle for a negative gradient Recover an angle from the value of a trigonometric ratio Calculate the exact midpoint by averaging corresponding coordinates Recover one endpoint exactly from the other endpoint and the midpoint by reflecting coordinate-wise about the midpoint Calculate the exact squared distance and then the distance between two points, retaining a surd internally and rounding only when asked Identify the hypotenuse and compute it from the two shorter sides Form the line through a segment's midpoint with the perpendicular gradient, including horizontal and vertical segments