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

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.

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?

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Problem solving with graphing linear relationships

Lesson outcome