ExpertEasy1 markMultiple Choice
AQA GCSE · Question 15.1 · Algebra
This question is about what happens to the value of y when the value of x is doubled in different equations.
For the equation y = 8x, what happens to the value of y when x is doubled?
This question is about what happens to the value of y when the value of x is doubled in different equations.
For the equation y = 8x, what happens to the value of y when x is doubled?
Answer options:
A.
The value of y is doubled
B.
The value of y is divided by 4
C.
It is not possible to say what happens to the value of y
D.
The value of y is multiplied by 4
E.
The value of y is halved
How to approach this question
1. Take the original equation, y = 8x.
2. Replace x with (2x) to represent doubling x.
3. The new equation becomes y_new = 8(2x).
4. Simplify the new equation: y_new = 16x.
5. Compare the new value of y (16x) with the original value of y (8x).
6. Describe the change.
Full Answer
A.The value of y is doubled✓ Correct
The value of y is doubled.
We are testing the effect of doubling x on the equation y = 8x.
Let's pick a starting value for x, for example, x = 10.
The original y would be y = 8 * 10 = 80.
Now, let's double x. The new x is 2 * 10 = 20.
The new y will be y = 8 * 20 = 160.
Comparing the new y (160) to the original y (80), we see that 160 = 2 * 80. The value of y has doubled.
Algebraically:
Original: y = 8x
New x: x_new = 2x
New y: y_new = 8(x_new) = 8(2x) = 16x.
Since the original y was 8x, the new y (16x) is 2 * (8x), which is double the original y.
Common mistakes
✗ Confusing direct and inverse proportion.
✗ Incorrectly handling the algebra, e.g., thinking 8(2x) is 8+2x.
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