The graph of y – x against y + x is as shown below. (All graphs in this question are drawn to scale and the same scale has been used on each axis). Then, which of the options given shows the graph of y against x.
Explanation:
All the given graphs are drawn to the same scale.
We can see that the line makes an angle which is more than 45° with the horizontal axis.
∴ The slope of the line is greater than 1.
Let the slope be k.
∴ (y – x) = k(y + x) {∵ k > 1}
∴ y – x = ky + kx
∴y=x(k+1)(1-k)
(k+1)(1-k) is negative and (k+1)(1-k)>1
∴ The graph of y against x will be such that when x is positive, y is negative and |x| < |y|, except at (0, 0).
Hence, option (d).
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