The equation of a straight line

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.

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

a numerical multiplier of a specific variable in a term

the coordinate where a line crosses the $$y$$ axis

a relationship which, when plotted, forms a straight line

Which of these relationships are represented by this bar model?

gradient $$1\over 2$$, $$y$$-intercept $$(0,-2)$$

gradient $$1\over 2$$, $$y$$-intercept $$(0,2)$$

gradient $$-2$$, $$y$$-intercept $$(0,-2)$$

gradient $$-{1\over 2}$$, $$y$$-intercept $$(0,2)$$

gradient $$2$$, $$y$$-intercept $$(0,-2)$$

The graph shows 5 lines labelled A, B, C, D and E. Match the line to its gradient and $$y$$ intercept.

gradient $$5$$, $$y$$-intercept $$(0,-4)$$

gradient $$-5$$, $$y$$-intercept $$(0,4)$$

gradient $$-4$$, $$y$$-intercept $$(0,-5)$$

gradient $$4$$, $$y$$-intercept $$(0,5)$$

gradient $$5$$, $$y$$-intercept $$(0,4)$$

gradient $$-4$$, $$y$$-intercept $$(0,5)$$

Match the equations of lines to their key features. 

gradient $$15$$, $$y$$-intercept $$(0,-6)$$

gradient $$6$$, $$y$$-intercept $$(0,-15)$$

gradient $$-2$$, $$y$$-intercept $$(0,15)$$

gradient $$-2$$, $$y$$-intercept $$(0,5)$$

gradient $$-6$$, $$y$$-intercept $$(0,15)$$

What are the key features of the graph with equation $$y= 3(5 - 2x)$$ ?

Which coordinates are on the line $$2x - y = 5$$ ?

Which equations are represented by the bar model shown?

Fill in the missing value for the $$y$$  intercept of this line $$(0,$$ {{ }}$$)$$.

Match up the coordinate with the relationship it satisfies.

Match up the expressions containing brackets with their expanded forms. 

Fill in this coordinate, $$(5,$$ {{ }}$$)$$, so it satisfies the equation $$2x + 2y = 10$$.  

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