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A graph is drawn below - OCR - GCSE Maths - Question 21 - 2017 - Paper 1

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

Worked Solution & Example Answer:A graph is drawn below - 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

The graph does not pass through the origin (0, 0), which indicates that y is not directly proportional to x. In direct proportionality, when x equals zero, y must also be zero. Since the line starts above the origin, this confirms the lack of direct proportionality.

Step 2

Work out q when r is 25.

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Answer

Since q is directly proportional to r, we can express this relationship as:

q=kimesrq = k imes r

Where k is the constant of proportionality. To find k, we use the information given:

When r = 20, q = 68:

68=kimes2068 = k imes 20

Solving for k gives:

k=6820=3.4k = \frac{68}{20} = 3.4

Now, we can find q when r is 25:

q=3.4×25=85q = 3.4 \times 25 = 85

Thus, q when r is 25 is 85.

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