Substitute means to put in place of another.  In Algebra, substitution can be used to replace variables with values.

Checking and securing plotting a relationship

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

All of these coordinates fit the relationship $$x+y=5$$. This is an example of a {{ }} relationship.

What is the relationship between the $$x$$ and $$y$$ coordinates for the set $$(-1,-2)$$, $$(0,0)$$, and $$(1,2)$$?

Yes. This is an increasing linear relationship.

It's impossible to know until we plot them.

If we plot these coordinates will we see a linear relationship? $$(0,3)$$, $$(1,4)$$, $$(2,5)$$, $$(3,7)$$, and $$(4,7)$$.

Match the coordinates to the respective rule.

These coordinates all fit the relationship $$y=2x^2$$. Which words describe this relationship?

Some pupils are sharing $$36$$ sweets. As the number of pupils ($$p$$) varies, the numbers of sweets ($$s$$) each student gets varies. Which of the below represents this relationship?

In algebra, when we replace variables with values we call this {{ }}.

The $$y$$-coordinate is double the $$x$$-coordinate.

The $$y$$-coordinate is half the $$x$$-coordinate.

The $$y$$-coordinate is $$2$$ more than the $$x$$-coordinate.

The $$x$$-coordinate and $$y$$-coordinate sum to $$4$$.

Which statements are true of this coordinate?

What is the value of the expression $$5x-1$$ when $$x=3$$?

What is the value of the expression $$5x-1$$ when $$x=-3$$?

Starting with the lowest, order the value of these expressions when $$x=2$$.

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