A straight line is fitted to ( x,y) data. It crosses the horizontal axis at x=0.1 and has slope −0.02. Its fitted y at x=5 is

GATE 2016 EC (EC3) – Question 10

A straight line is fitted to $(\ln x,y)$ data. It crosses the horizontal axis at $\ln x=0.1$ and has slope −0.02. Its fitted y at x=5 is

Show answer and explanation

Correct answer: (A) −0.030

The horizontal coordinate is ln x, not x. With horizontal intercept 0.1 and slope −0.02, the fitted line is $y=-0.02(\ln x-0.1)$.

At x=5, ln5≈1.609438, giving y≈−0.0301888. Rounded to the listed precision this is **−0.030, A**.

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