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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?
Most Upvoted Answer
A straight line is fit to a data set (ln x, y) . This line intercepts ...
-0.02.
The equation of the line can be written as:
ln y = -0.02 ln x + b
where b is the y-intercept of the line.
To find b, we can use the fact that the line intercepts the abscissa at ln x = 0.1. This means that when ln x = 0.1, ln y = 0, since the line intercepts the x-axis at ln x = 0.1.
Plugging in these values into the equation of the line, we get:
0 = -0.02(0.1) + b
Solving for b, we get:
b = 0.002
Therefore, the equation of the line is:
ln y = -0.02 ln x + 0.002
The equation of the line can be written as:
ln y = -0.02 ln x + b
where b is the y-intercept of the line.
To find b, we can use the fact that the line intercepts the abscissa at ln x = 0.1. This means that when ln x = 0.1, ln y = 0, since the line intercepts the x-axis at ln x = 0.1.
Plugging in these values into the equation of the line, we get:
0 = -0.02(0.1) + b
Solving for b, we get:
b = 0.002
Therefore, the equation of the line is:
ln y = -0.02 ln x + 0.002
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Community Answer
A straight line is fit to a data set (ln x, y) . This line intercepts ...
General equation of a line is:-
y = mx + c for (x,y)
for this problem the eq. is y = m(lnx) + c
where m = slope of line
and c = intercept of line on y-axis
Now, it is given that the line intercepts abscissa (x-axis) at lnx = 0.1.
So, putting y = 0 and lnx = 0.1 in eq. of line, we get
0 = -0.02 (0.1) + c
so, we get c = 0.002
So, the eq. of line becomes y = -0.02 (lnx) + 0.002
putting x = 5 , we get
y = -0.02(ln5) + 0.002 = -0.0301
Hence, option (a) is correct.
y = mx + c for (x,y)
for this problem the eq. is y = m(lnx) + c
where m = slope of line
and c = intercept of line on y-axis
Now, it is given that the line intercepts abscissa (x-axis) at lnx = 0.1.
So, putting y = 0 and lnx = 0.1 in eq. of line, we get
0 = -0.02 (0.1) + c
so, we get c = 0.002
So, the eq. of line becomes y = -0.02 (lnx) + 0.002
putting x = 5 , we get
y = -0.02(ln5) + 0.002 = -0.0301
Hence, option (a) is correct.
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