The rate of change is how one variable changes with respect to another. If constant, there is a linear relationship.

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

Problem solving with graphing linear relationships

Maths

Checking and securing understanding of plotting coordinates

Checking and securing understanding of plotting coordinates generated from a rule

Checking and securing understanding of plotting coordinates with technology

Checking and securing plotting a relationship

Features of linear relationships

Defining features of linear relationships

Positive rate of change from a graph

Negative rate of change from a graph

Rate of change from a coordinate pair

The intercept point

The equation of a straight line

Finding the equation of the line y = mx + c

Finding the equation of the line ay + bx + c = 0

Using dynamic software to explore linear relationships

In this unit, pupils saw that an arithmetic sequence can be represented graphically and that this is a linear relationship. Any point on the line satisfies this relationship. In the future unit, pupils learn how to find a value that satisfies the relationship when the second value is known, without the aid of the graph.

The sequences unit allowed pupils to explore different ways of generating sequences and then representing an arithmetic sequence graphically. This served as an introduction to this unit on graphical representations of linear equations.

In this unti we develop understanding of linear relationships and explore the key features of a linear equation such as the gradient, intercept and determining an equation from coordinate pairs.

Graphical representations of linear equations

On a time distance graph a greater speed is represented by a steeper {{ }}.

They cost the same price for that many miles.

The graph shows the cost of two taxi companies for miles travelled. Which firm is cheapest for a $$3$$ mile journey?

The graph shows the cost of two taxi companies for miles travelled. At how many miles do they cost the same price?

The graph shows the cost of two taxi companies for miles travelled. How much do firm A charge per mile in $$£$$?

This graph shows the time $$(t)$$ and distance $$(d)$$ of a car journey. For how long did the car stop?

This graph shows the time $$(t)$$ and distance $$(d)$$ of a car journey. When is the car moving fastest?

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

Which of the values are missing from the table of values for the first five terms of the sequence $$7n-10$$?

A pupil is saving money. They start with $$£30$$ and save $$£8$$ per week. How much will they have after $$5$$ weeks?

At what coordinates do these two lines intersect?

Which of these lines has the steeper gradient?

Yes. The $$y$$ values have a constant difference of $$+5$$.

No. Both variables are not changing at a constant rate.

Will this table of values plot a linear relationship?

Starter Quiz

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