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A straight line is fit to a data set (ln x, y) . This line intercepts the abscissa at ln x = 0.1 and has a slope of −0.02. What is the value of y at x = 5 from the fit?
  • a)
    −0.030
  • b)
    −0.014
  • c)
    0.014
  • d)
    0.030
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A straight line is fit to a data set (ln x, y) . This line intercepts ...
The equation of a line is

y = mx + c where m is the slope & c is the y-intercept

Now, In this question x is replaced with lnx

So, the equation of line becomes,

y = mlnx + c

or, y = -0.02lnx + c

We have given with abscissa which is essentially x-intercept. So, now we have to find ‘c’ the y-intercept.

for, y=0, lnx = 0.1 (given in the question)

Putting the value,

0 = -0.02 x 0.1 + c

or, c = 0.002

So, the equation of line becomes,

y = -0.02lnx + 0.002

putting x = 5 (asked in the question)

y = -0.002ln5 + 0.002 = -0.002 x 1.6 + 0.002 = -0.03

(ln5 = 1.6)
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A straight line is fit to a data set (ln x, y) . This line intercepts the abscissa at ln x = 0.1 and has a slope of −0.02. What is the value of y at x = 5 from the fit?a)−0.030b)−0.014c)0.014d)0.030Correct answer is option 'A'. Can you explain this answer?
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