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.

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

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

Parallel linear graphs

Maths

Checking and securing understanding of drawing vertical and horizontal graphs

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

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

Five lines have been drawn on the same graph. Which of these lines is parallel to line A (black)?

Match each equation of a line to an equation of a line that is parallel to it.

Which of these equations will produce a line that is parallel to the line with equation $$5y - 2x = 15$$ ?

The line with equation $$y =$$ {{}} $$- 2x$$ passes through the point (1, 4) and is parallel to the line $$y = 7 - 2x$$.

Which of these is the equation of the line which goes through the point (10, 20) and is parallel to the line $$y = {5\over 2}x + 1$$?

A line passing through coordinates (2, 6) and (4, 9)

A line passing through coordinates (-5, 1) and (-7, 4)

A line passing through coordinates (0, 1) and (6, 10)

The line with equation $$y = {3\over 2}x$$

The line with equation $$y ={2\over3} x$$

The line L passes through the points with coordinates (3, 7) and (5, 10). Which of these lines are parallel to the line L?

Which of these best completes the definition of parallel: 'Two lines are parallel if they are straight lines which...'?

Match the equation of each straight line to its gradient. 

The gradient of the line shown on this graph is {{ }}.

Which of these coordinates are on the line $$y = -x - 5$$ ?

What is the gradient of the line with equation $$3y + 4x - 8 = 0$$ ?

A line passes through the points with coordinates (-3, 4) and (5, -12). The gradient of this line is {{ }}.

Starter Quiz

Which of these best completes the definition of parallel: 'Two lines are parallel if they are straight lines which...'?