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

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

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

Problem solving with graphing 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

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 $$x=2$$.

Checking and securing plotting a relationship

Lesson outcome