Question

In an experiment, water in a flask is heated. The temperature of water is recorded over time at intervals of $30$ seconds as tabulated below.
Time (minutes) Temperaure (${}^{o}C$)

$0$	$25$
$0.5$	$45$
$1$	$70$
$1.5$	$90$
$2$	$100$

Plot a scatter plot and choose the correct option for the equation of line of best fit.

• A. $y-45=0.5(x-0.5)$
• B. $y-0.5=45(x-0.5)$
• C. $y-0.5=45(x-45)$
• D. $y-45=45(x-0.5)$

Answer 1

The correct option is D $y-45=45(x-0.5)$

Let's plot the temperature of water (dependent variable) on the vertical axis, and time (independent variable) on the horizontal axis.

As per the given data, the scatter plot becomes


Here, the line, which connects the points $(0.5,45)$ and $(1.5,90)$, best fits the trend of the graph.

$\therefore$ The cyan line in the above scatter plot is the line of best fit.

The slope of the line which passess through the points $(x_1,y_1)$ and $(x_2,y_2)$ is
$m=\frac{y_2-y_1}{x_2-x_1}$

In our scatter plot,
$(x_1,y_1)=(0.5,45)$
and
$(x_2,y_2)=(1.5,90)$

$\therefore m=\frac{90-45}{1.5-0.5}=\frac{45}{1}=45$

Hence, the equation of the line of best fit is

$y-y_1=m(x-x_1)$

$\Rightarrow y-45=45(x-0.5)$

$\therefore$ Option (d.) is the correct one.