Algebraic Expressions For Directly Proportional Relationships Lesson | GCSE Maths Edexcel IGCSE Higher

Algebraic Expressions For Directly Proportional Relationships

This lesson covers:

How to express directly proportional relationships as an algebraic equation
How to use these equations to solve problems

$q$ is directly proportional to $p$ . When $q$ is 24, $p$ is 8.

Find a formula for $q$ in terms of $p$ . Give your answer in the form $q$ = $kp$ .

q=3p|Q=3P|3p=q

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Find $q$ when $p$ is 16.

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Find $p$ when $q$ is 46.5.

15.5

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The weight ( $W$ ) of a piece of wire is directly proportional to its length ( $L$ ). A piece of wire is 27 cm long ( $L$ ) and has a weight ( $W$ ) of 6 grams.

Write an algebraic equation that links the wires length ( $L$ ) to its weight ( $W$ ). Give your answer in the form $L$ = $kW$ , where k is a constant to be found.

L=4.5W|l=4.5w

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Another piece of the same wire has a weight of 14g. How long must the piece of wire be?

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A third piece of the same wire has a length of 36cm. What is the weight of the piece of wire?

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In a spring, the force ( $F$ newtons) is directly proportional to its extension ( $e$ cm).

When the tension is 150 newtons, the extension is 6 cm.

Find a formula for $F$ in terms of $e$ . Give your answer in the form $F$ = $ke$ .

F=25e|f=25e|F=25E

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Calculate the force, in newtons, when the extension is 2.4 cm.

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Calculate the extension, in cm, when the force is 350 newtons.

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