Algebra — AQA GCSE Practice Question 15.2

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1. Take the original equation, y = 10/x. 2. Replace x with (2x) to represent doubling x. 3. The new equation becomes y_new = 10/(2x). 4. Rearrange the new equation: y_new = (1/2) * (10/x). 5. Compare the new value of y with the original value of y (10/x). 6. Describe the change.

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E.The value of y is halved✓ Correct

The value of y is halved.

We are testing the effect of doubling x on the equation y = 10/x. This is an example of inverse proportion. Let's pick a starting value for x, for example, x = 10. The original y would be y = 10 / 10 = 1. Now, let's double x. The new x is 2 * 10 = 20. The new y will be y = 10 / 20 = 0.5. Comparing the new y (0.5) to the original y (1), we see that 0.5 is half of 1. The value of y has halved. Algebraically: Original: y = 10/x New x: x_new = 2x New y: y_new = 10/(x_new) = 10/(2x) = (1/2) * (10/x). Since the original y was 10/x, the new y is (1/2) * y, which is half the original y.

Common mistakes

✗ Thinking that doubling x will double y. This is true for direct proportion, not inverse proportion. ✗ Thinking the value is divided by 2, which is the same as halved, but selecting a different option.

For the equation y = 10/x, what happens to the value of y when x is doubled?

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