The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

The gradient is a measure of how steep a line is.

An intercept is the coordinate where a line or curve meets a given axis.

Checking and securing understanding of drawing vertical and horizontal graphs

Maths

Checking and securing understanding of finding the equation of the line from the graph

Checking and securing understanding of finding the equation of the line from coordinates

Parallel linear graphs

Perpendicular linear graphs

Identifying perpendicular linear graphs

Parallel and perpendicular lines on coordinate axes

Ratios in line segments on coordinate axes

Checking and understanding graphs showing direct proportion

Graphs showing inverse proportion

Advanced problem solving with linear graphs

The work on gradient in this unit is expanded further in the future unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

In the prior unit, pupils drew a linear graph from its equation and related the features of the graph to its equation. In this unit, pupils consider equations that produce parallel or perpendicular graphs and how their equations relate to each other.

In this unit pupils consider equations that produce parallel or perpendicular graphs and how their equations relate to each other.

Linear graphs

The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction.

Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.

Two lines are perpendicular if they meet at right angles.

IFF (If and only if) is an implication that goes both ways.

An irrational number is one that cannot be written in the form a/b where a and b are integers and b is not equal to 0

A surd is an irrational number expressed as the root of a rational number.

The midpoint of a line segment is halfway between the two end points.

Two variables are in direct proportion if they have a constant multiplicative relationship.

Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.

The tangent (of a circle) is a line that intersects the circle exactly once.

Linear graphs

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