The gradient is a measure of how steep a line is

Expressions contain one or more terms, where each term is separated by an operator.

An equation is used to show that one number or calculation is equal to another.

The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

Different types of equations

Maths

In this unit, pupils learn how to rearrange an equation to find a specific value that satisfies the equation. In expressions and formulae, pupils use their understanding of rearrangement to change the subject of a formula.

In the prior 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 this unit, pupils learn how to find a value that satisfies the relationship when the second value is known, without the aid of the graph.

In this unit pupils will learn how to find a value that satisfies a linear relationship when one value is known both with a single step operation, and multiple step operations. A variety of cases are explored including using brackets and rearranging.

Solving linear equations

Which of these equations are linear? The graphs of the equations are shown.

Which is the correct graph of the expression $$2 − 4t$$ as $$t$$ varies? The table of values for $$2 − 4t$$ is shown.

The table of values for $$y = {30\over x}$$ is shown. The missing value is {{ }}.

Select the correct graph of the expression $$y = {x^3} − 5$$. The table of values for $$y = {x^3} − 5$$ is shown.

The table of values for $$ 2x + y = 5(x − 1)$$ is shown. The missing value is {{ }}.

The table of values for $$ xy = 12$$ is shown. The missing value is {{ }}.

the $$x$$ value where the line crosses the $$x$$-axis

the vertical distance from the origin to the line

Which of these is the best description of the gradient of a line?

Select the coordinates that lie on the line $$y = 2x − 3$$.

The table shows values for the equation $$y = 5 − 3x$$. The missing number is {{ }}.

When the equation of a straight line is written in the form $$y = mx + c$$, ($$m$$) is the coefficient of $$x$$ and represents the {{ }}.

Work out the value of $$y$$ that satisfies the equation $$3x + y = 6(x − 2)$$ when $$x = 5$$. $$y =$$ {{ }}

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