GATE ECE 2016 Set 3 | GA | Question: 10

Question

A straight line is fit to a data set $(\text{ln }x,y).$ This line intercepts the abscissa at $\text{ln } x =0.1$ 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. $0.030$

Comments

Key points:

• We have a straight line fitted to data points where the $x$-axis is "$ln \, x$" and the $y$-axis is just "$y$".
• "Abscissa" is just another word for the $x$-axis.

Answer 1

Interception at $x-$axis is $\ln \  x=0.1$ and slope $=-0.02$

Equation fo straight line is given by,

$y=mx+C$

According to the question,

$y=m(\ln \ x)+C$ where $m=-0.02$

$y=-0.02(\ln \ x)+C\quad \rightarrow(1)$

Abscissa is known as intercept in $x-$axis i.e. for $y=0,\ln \ x =0.1$

From equation $(1),$

$0=-0.02\times 0.1+C$

$C=0.002\quad \rightarrow(2)$

From equations $(1)$ and $(2),$

$y=-0.02(\ln \ x)+0.002$

At $x=5,$

$y=-0.02(\ln \ 5)+0.002$

$y=-0.030$

So, the correct answer is $(A).$

Comments

$\log_{e} 5 = \ln 5 = 1.609$

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A straight line is fit to a data set (In x, y). This line intercepts the abscissa at In x = 0.1

lnx, y. I misread the question and I didnt quite understand why did we use ln x 

Posting it here so anyone can get a better idea.

Answer 2

The equation of straight line with slope and the coordinates (x,y) is Y=mX+C  where “C” is constant. Since the graph is plotted in Y against Ln x   so the above equation modifies as Y=m LnX + C. All points are given and we can find the constant “C’. Hence option A is correct.