Question

In a science experiment, the weights of different body masses were measured at a specific height from the sea level as tabulated below.
Mass (kg) Weight $\left({\text{kg}\times \text{m/second}}^2\text{or Newton (N)}\right)$

$2$	$19.6$
$4$	$40$
$6$	$58.8$
$8$	$76$

Choose the correct equation for the line of best fit.

• A. $y-40=10(x-4)$
• B. $y-19.6=9.8(x-2)$
• C. $y-2=9.8(x-19.6)$

Answer 1

The correct option is B $y-19.6=9.8(x-2)$

Let's plot the mass (independent variable) on the horizontal axis and corresponding weight (dependemt variable) on the vertical axis.


In the above scatter plot, if the line passes through the points $(2,19.6)$ and $(6,58.8)$, all the remaining data points will be equally divided around the line. Also, the line depicts the trend of the data set accurately.

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

Here, in the scatter plot,
$(x_1,y_1)=(2,19.6)$
and
$(x_2,y_2)=(6,58.8)$

$\therefore m=\frac{58.8-19.6}{6-2}=\frac{39.2}{4}=9.8$

Hence, the equation of the line of best fit is

$y-y_1=m(x-x_1)$
$\Rightarrow y-19.6=9.8(x-2)$

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