**Core concept 4.2 **

**Graphical representations**

4.2.1.1 Describe and plot coordinates, including non-integer values, in all four quadrants

4.2.1.2 Solve a range of problems involving coordinates

**4.2.1.3* Know that a set of coordinates, constructed according to a mathematical rule, can be represented algebraically and graphically**

4.2.1.4 Understand that a graphical representation shows all of the points (within a range) that satisfy a relationship

**4.2.1.3 Know that a set of coordinates, constructed according to a mathematical rule, can be represented algebraically and graphically**

**4.2.1.3 Know that a set of coordinates, constructed according to a mathematical rule, can be represented algebraically and graphically**

●Identify an additive relationship from a set of coordinates.

●Understand how many points are required to determine a linear relationship.

●Identify a multiplicative relationship from a set of coordinates.

●Visualise the relationship between sets of coordinates.

●Identify a two-step relationship from a set of coordinates.

●Solve problems where there is more than one answer and there are elements of experimentation, investigation, checking, reasoning, proof, etc.

**Example 1**

**Example 4**

Change the coordinates and then move the sliders to make the line go through all the coordinates.

4.2.2.1 Recognise that linear relationships have particular algebraic and graphical features as a result of the constant rate of change

4.2.2.2 Understand that there are two key elements to any linear relationship: rate of change and intercept point

**4.2.2.3* That writing linear equations in the form y = mx + c helps to reveal the structure**

4.2.2.4 Solve a range of problems involving graphical and algebraic aspects of linear relationships

**4.2.2.3 That writing linear equations in the form y = mx + c helps to reveal the structure**

**4.2.2.3 That writing linear equations in the form y = mx + c helps to reveal the structure**

●The value of the constant term is the y-intercept when the equation is in the form y = mx + c.

●Equations with a y-intercept of zero pass through the origin.

●The value of the coefficient of x is the gradient, when the equation is in the form y = mx + c.

●Identify the gradient and the y-intercept from equations in various forms.

Which of the following points lie on the line 2*x* + *y* = 7:

(1,5) (5,1) (3,1) (4,1) (5,3) (5,-3)?

Can you explain why or why not?

Can you show this with a calculation as well as a drawing?

**y = mx**

**y = mx**

**y = mx+c**

**y = mx+c**

The graphs above allow you to make connections between the bar model (algebra tile), graph, coordinates and table.

The graphs below clearly show the gradient as steps. A similar activity can be done with Cuisenaire rods square paper.

4.2.3.1 Understand that different types of equation give rise to different graph shapes, identifying quadratics in particular

4.2.3.2 Read and interpret points from a graph to solve problems

**4.2.3.3 Model real-life situations graphically**

**4.2.3.4 Recognise that the point of intersection of two linear graphs satisfies both relationships and hence represents the solution to both those equations**

**4.2.3.3 Model real life situations graphically**

**4.2.3.3 Model real life situations graphically**

●Understand and interpret the gradient in context.

●Understand and interpret the intercept in context.

●Understand and interpret a graph in context.

For real life graphs try Turtle Time Trials from Desmos

**4.2.3.4 Recognise that the point of intersection of two linear graphs satisfies both relationships and hence represents the solution to both those equations**

**4.2.3.4 Recognise that the point of intersection of two linear graphs satisfies both relationships and hence represents the solution to both those equations**

●Identify regions on the plane

●Understand that the point of intersection is a solution to both equations