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A graph is drawn below: Explain how you know that y is not directly proportional to x - OCR - GCSE Maths - Question 21 - 2017 - Paper 1

Question 21

A graph is drawn below: Explain how you know that y is not directly proportional to x. q is directly proportional to r. q is 68 when r is 20. Work out q when r is... show full transcript

Worked Solution & Example Answer:A graph is drawn below: Explain how you know that y is not directly proportional to x - OCR - GCSE Maths - Question 21 - 2017 - Paper 1

Step 1

Explain how you know that y is not directly proportional to x.

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Answer

To determine whether y is directly proportional to x, we check if the line passes through the origin (0, 0). In the given graph, the line does not intersect the origin, indicating that there is a constant addition to y as x changes. This lack of passage through the origin confirms that y is not directly proportional to x.

Step 2

Work out q when r is 25.

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Answer

Since q is directly proportional to r, we can use the constant of proportionality. We know that q = k * r, where k is the constant. First, we calculate k using the values q = 68 when r = 20:

$k = \frac{q}{r} = \frac{68}{20} = 3.4$

Now, to find q when r = 25:

$q = k * r = 3.4 * 25 = 85$ .

Therefore, when r is 25, q is 85.

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